Apparatus and method for channel coding in communication system

ABSTRACT

This application relates to communicating information between communication devices. A channel coding method is disclosed. A communication device obtains an input sequence of K bits. The communication device encodes the input sequence using a low density parity check (LDPC) matrix H, to obtain an encoded sequence. The LDPC matrix H is determined according to a base matrix and a lifting factor Z. The base matrix includes m rows and n columns, m is greater than or equal to 5, and n is greater than or equal to 27. The lifting factor Z satisfies a relationship of 22*Z≥K. According to the encoding method provided in the embodiments, information bit sequences of a plurality of lengths can be encoded for transmission between the communication devices.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/161,539, filed on Jan. 28, 2021, which is a continuation of U.S.patent application Ser. No. 16/584,911, filed on Sep. 26, 2019, now U.S.Pat. No. 10,924,134, which is a continuation of U.S. patent applicationSer. No. 16/205,186, filed on Nov. 29, 2018, now U.S. Pat. No.10,432,219, which is a continuation of International Application No.PCT/CN2017/092877, filed on Jul. 13, 2017. The International ApplicationPCT/CN2017/092877 claims priority to International Application No.PCT/CN2017/090417, filed on Jun. 27, 2017, International PatentApplication No. PCT/CN2017/087943, filed on Jun. 12, 2017, InternationalPatent Application No. PCT/CN2017/087830, filed on Jun. 9, 2017,International Patent Application No. PCT/CN2017/087073, filed on Jun. 2,2017, International Patent Application No. PCT/CN2017/086227, filed onMay 26, 2017, Chinese Patent Application No. 201710381396.2, filed onMay 25, 2017, and Chinese Patent Application No. 201710314217.3, filedon May 5, 2017. All of the aforementioned patent applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

Embodiments of the present application relate to the communicationsfield, and in particular, to apparatuses and methods for channel codingin communication systems.

BACKGROUND

Low density parity check (LDPC) code is a type of linear block codehaving a sparse check matrix, and is characterized by flexible structureand low decoding complexity. Because decoding the LDPC code uses apartially parallel iterative decoding algorithm, the LDPC code has ahigher throughput than a conventional turbo code. The LDPC code can beused as an error-correcting code in a communication system, so as toincrease channel transmission reliability and power utilization. LDPCcodes may be further widely used in space communications, fiber opticcommunications, personal communication systems, Asymmetrical DigitalSubscriber Loop (ADSL), magnetic recording devices, and the like. TheLDPC code has been currently considered as one of channel coding modesin the fifth generation (5G) mobile communication systems.

In actual applications, LDPC matrices having different specialstructures may be used. A LDPC matrix H, characterized by a specialstructure, may be obtained by expanding an LDPC base matrix having aquasi cyclic (QC) structure. QC-LDPC coding scheme is suitable forhardware with high parallelism, and provides a higher throughput.Furthermore, it is possible to design a LDPC matrix that is suitable forchannel coding.

SUMMARY

Embodiments of the present application provide an information processingmethod, a communications apparatus, and a communications system, tosupport encoding and decoding of information bit sequences of variouslengths and meet flexible code length and code rate requirements of thecommunication system.

According to a first aspect, an encoding method and an encoder areprovided, and the encoder encodes an input sequence by using a lowdensity parity check (LDPC) matrix.

According to a second aspect, a decoding method and a decoder areprovided, and the decoder decodes an input sequence by using a lowdensity parity check (LDPC) matrix.

In a first implementation of the first aspect or the second aspect, abase graph of the LDPC matrix is represented by a matrix of m rows and ncolumns, m is an integer greater than or equal to 5, and n is an integergreater than or equal to 27. The base graph includes at least asubmatrix A and a submatrix B. The submatrix A is a matrix of five rowsand 22 columns. The submatrix B is a matrix of five rows and fivecolumns, and the submatrix B includes a column whose weight is 3 and asubmatrix B′ with a bi-diagonal structure.

Optionally, in the submatrix A, one column has a weight of 5, one columnhas a weight of 4, and other 20 columns have a weight of 3.

Optionally, in the submatrix B, one column has a weight of 3, and threecolumns have a weight of 2.

Based on the foregoing implementation, the submatrix B further includesone column whose weight is 1.

In a second implementation of the first aspect or the second aspect, abase graph of the LDPC matrix is represented by a matrix of m rows and ncolumns, m is an integer greater than or equal to 5, and n is an integergreater than or equal to 27. The base graph includes at least asubmatrix A and a submatrix B. The submatrix A is a matrix of five rowsand 22 columns; and the submatrix B is a matrix of five rows and fivecolumns. In a matrix including the submatrix A and the submatrix B, onecolumn has a weight of 5, one column has a weight of 4, 21 columns havea weight of 3, three columns have a weight of 2, and one column has aweight of 1.

Optionally, in the matrix including the submatrix A and the submatrix B,one row has a weight greater than or equal to 1 and less than or equalto 5, and other four rows have weights greater than or equal to 17 andless than or equal to 21.

For example, in the matrix including the submatrix A and the submatrixB, one row has a weight of 3, and other four rows have a weight of 19.In this case, the matrix including the submatrix A and the submatrix Bmay include rows or columns in a matrix block of five rows thatcomprises row 0 to row 4 and column 0 to column 26 in a base graph 30 ashown in FIG. 3 a . The rows can be switched with each other, and thecolumns can also be switched with each other. For example, in the matrixblock including the submatrix A and the submatrix B in the base graph 30a, row 3 and row 0 may be switched with each other, row 2 and row 1 maybe switched with each other, and column 23 and column 25 may be switchedwith each other, to obtain a core matrix in a base graph 80 a shown inFIG. 8 a.

Based on the foregoing implementations, a part that is in a base matrixof the LDPC matrix and that corresponds to the submatrix A and thesubmatrix B may be represented by, for example, any one of base matrices30 b-1, 30 b-2, 30 b-3, 30 b-4, and 30 b-5 shown in FIGS. 3 b -1, and 30b-6, 30 b-7, 30 b-8, 30 b-9, and 30 b-10 shown in FIG. 3 b -2.

A part that is in a base matrix of the LDPC matrix and that correspondsto the submatrix A and the submatrix B may be represented by a matrixobtained by performing column permutation, row permutation, or rowpermutation and column permutation on any one of the base matrices 30b-1, 30 b-2, 30 b-3, 30 b-4, 30 b-5, 30 b-6, 30 b-7, 30 b-8, 30 b-9, or30 b-10. For example, the part that is in the base matrix of the LDPCmatrix and that corresponds to the submatrix A and the submatrix B mayinclude rows or columns in any one of the base matrices 30 b-1, 30 b-2,30 b-3, 30 b-4, 30 b-5, 30 b-6, 30 b-7, 30 b-8, 30 b-9, or 30 b-10.

Based on the foregoing implementations, a part that is in a base matrixof the LDPC matrix and that corresponds to the submatrix A and thesubmatrix B may be represented by any one of base matrices 80 b-1, 80b-2, 80 b-3, 80 b-4, 80 b-5 shown in FIG. 8 b -1, or 80 b-6 shown inFIG. 8 b -2. 80 b-4 is a matrix obtained by performing row permutationand column permutation on 30 b-3, 80 b-5 is a matrix obtained byperforming row permutation and column permutation are performed on 30b-4, and 80 b-6 is a matrix obtained by performing row permutation andcolumn permutation are performed on 30 b-5.

To support different block lengths, an LDPC code needs different liftingfactors Z. Based on the foregoing implementations, in a possibleimplementation, base matrices corresponding to different lifting factorsZ are used based on the different lifting factors Z.

For example,

if the lifting factor Z is one of {16, 18, 20, 22, 24, 26, 28, 30}, apart that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 30 b-1 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {32, 36, 40, 44, 48, 52, 56, 60}, apart that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 30 b-2 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 30 b-3 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 30 b-4 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in a base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be the base matrix 30 b-5 shown inFIG. 3 b -1.

In another possible implementation,

if the lifting factor Z is one of {24, 26, 28, 30}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be the base matrix 80 b-1 shown in FIG. 8 b-1; or

if the lifting factor Z is one of {32, 36, 40, 44}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be the base matrix 80 b-2 shown in FIG. 8 b-1; or

if the lifting factor Z is one of {48, 52, 56, 60}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be the base matrix 80 b-3 shown in FIG. 8 b-1; or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, a part that is in a base matrix of the base graph 80 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 80 b-4 shown in FIG. 8 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in a base matrix of the base graph 80 a and thatcorresponds to the submatrix A and the submatrix B may be the basematrix 80 b-5 shown in FIG. 8 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in a base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be the base matrix 80 b-6 shown inFIG. 8 b -2.

In another possible implementation, the submatrix A may further includetwo columns of built-in puncture bits.

Further, to obtain a flexible code rate, a submatrix C, a submatrix D,and a submatrix E of corresponding sizes may be added based on a corematrix, to obtain different code rates.

The submatrix C is an all-zero matrix of five rows and m_(D) columns;

the submatrix D is a matrix of m_(D) rows and 27 columns;

the submatrix E is an identity matrix of M_(D) rows and M_(D) columns;and

m_(D) is an integer and 0≤m_(D)≤41.

The submatrix D includes m_(D) rows in a matrix F, the matrix F has 41rows and 27 columns, and weights of the rows in the matrix F arerespectively 7, 7, 9, 8, 7, 7, 8, 6, 6, 5, 6, 5, 5, 6, 5, 5, 5, 5, 4, 4,4, 5, 4, 5, 4, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 3, 3, and 4.

In a possible implementation, the matrix F is a matrix including row 5to row 45 and column 0 to column 26 in the base graph 30 a.

In a possible implementation, a shift matrix of the matrix F may berepresented by any one of base matrices 30 c-1 shown in FIG. 3 c -2, 30c-2 shown in FIG. 3 c -3, 30 c-3 shown in FIG. 3 c -4, 30 c-4 shown inFIG. 3 c -5, or 30 c-5 shown in FIG. 3 c -6.

In another possible implementation, row 17 and row 19 in the base graph30 a may be switched with each other, and column 39 and column 41 may beswitched with each other, to obtain the base graph matrix 80 a shown inFIG. 8 a . For another example, the submatrix D includes m_(D) rows in amatrix F, row permutation may not be performed between the m_(D) rows,or row permutation may be performed between one or more of the m_(D)rows, and the submatrix E still has a diagonal structure. For example,the submatrix D includes m_(D) rows in the matrix F, row 12 and row 14in the matrix F are switched with each other, and the submatrix E stillhas a diagonal structure, to obtain the base graph 80 a.

To support different block lengths, an LDPC code needs different liftingfactors Z. Based on the foregoing implementations, in a possibleimplementation, base matrices corresponding to different lifting factorsZ are used based on the different lifting factors Z. For example,

in a possible implementation,

if the lifting factor Z is one of {16, 18, 20, 22, 24, 26, 28, 30}, thesubmatrix D in the base matrix may include m_(D) rows in a shift matrix30 c-1 shown in FIG. 3 c -2; or

if the lifting factor Z is one of {32, 36, 40, 44, 48, 52, 56, 60}, thesubmatrix D in the base matrix may include m_(D) rows in a shift matrix30 c-2 shown in FIG. 3 c -3; or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, the submatrix D in the base matrix may include m_(D) rows in ashift matrix 30 c-3 shown in FIG. 3 c -4; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the submatrix D in the base matrix may include m_(D) rows in ashift matrix 30 c-4 shown in FIG. 3 c -5; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, thesubmatrix D in the base matrix may include m_(D) rows in a shift matrix30 c-5 shown in FIG. 3 c -6.

In another possible implementation, a lifting factor set may be {24, 26,28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112,120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384}.

If the lifting factor Z is one of {24, 26, 28, 30}, the shift matrix ofthe matrix F may be 80 c-1 shown in FIG. 8 c -2; or

if the lifting factor Z is one of {32, 36, 40, 44}, the shift matrix ofthe matrix F may be 80 c-2 shown in FIG. 8 c -3; or

if the lifting factor Z is one of {48, 52, 56, 60}, the shift matrix ofthe matrix F may be 80 c-3 shown in FIG. 8 c -4; or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, the shift matrix of the matrix F may be 80 c-4 shown in FIG. 8 c-5; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be 80 c-5 shown in FIG. 8 c-6; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be 80 c-6 shown in FIG. 8 c -7.

The base graph and the base matrix of the LDPC matrix in the firstimplementation can meet performance requirements of code blocks whoseblock lengths are 352 to 8448 bits.

Based on any one of the foregoing aspects or the possibleimplementations of the aspects, in another possible implementation, themethod further includes: determining a lifting factor Z. For example, avalue of the lifting factor Z is determined based on a length K of theinput sequence. For example, if the length of the input sequence is K, aminimum value that meets 22*Z≥K may be determined from a plurality oflifting factors defined in a system.

For a communications device at a transmit end, the encoding an inputsequence by using an LDPC matrix includes: encoding the input sequenceby using an LDPC matrix corresponding to the lifting factor Z.

For a communications device at a receive end, the decoding an inputsequence by using an LDPC matrix includes: decoding the input sequenceby using an LDPC matrix corresponding to the lifting factor Z.

Based on any one of the foregoing aspects or the possibleimplementations of the aspects, in another possible implementation, thebase matrix of the LDPC matrix may be stored in a memory.

Based on any one of the foregoing aspects or the possibleimplementations of the aspects, in another possible implementation, thebase graph of the LDPC matrix is stored in the memory, and a shift valueof a non-zero-element in the base matrix of the LDPC matrix may bestored in the memory.

Based on the foregoing possible implementations, in a possible design,at least one of a base graph and a base matrix for LDPC encoding ordecoding is obtained by performing row permutation, or columnpermutation, or row permutation and column permutation on at least oneof the base graph and the base matrix of the LDPC matrix.

According to a third aspect, a communications apparatus is provided, andthe apparatus may include software modules and/or hardware componentsconfigured to perform any one of the possible implementations of thefirst aspect in the foregoing method design.

In a possible design, the communications apparatus provided in the thirdaspect includes the encoder described in the first aspect, a determiningunit, and a processing unit. The determining unit is configured todetermine a lifting factor Z required for encoding an input sequence.The processing unit is configured to encode the input sequence by usingan LDPC matrix corresponding to the lifting factor Z.

Optionally, the communications apparatus further includes a transceiver,and the transceiver is configured to send a signal corresponding toencoded information data.

According to a fourth aspect, a communications apparatus is provided,and the apparatus may include a module configured to perform any one ofthe possible implementations of the second aspect in the foregoingmethod design. The module may be software and/or hardware.

In a possible design, the communications apparatus provided in thefourth aspect includes the decoder described in the second aspect, anobtaining unit, and a processing unit. The obtaining unit is configuredto obtain a soft value sequence of an LDPC code and a lifting factor Z.The processing unit is configured to decode the soft value sequence ofthe LDPC code based on a base matrix H_(B) corresponding to the liftingfactor Z, to obtain an information bit sequence.

The communications apparatus further includes a transceiver, and thetransceiver is configured to receive a signal including an LDPC code.

According to a fifth aspect, a communications apparatus is provided,including one or more processors.

In a possible design, the one or more processors may implement functionsof the encoder in the first aspect. In another possible design, theencoder in the first aspect may be a part of the processor, and theprocessor may implement other functions in addition to functions of theencoder in the first aspect.

In a possible design, the one or more processors may implement functionsof the decoder in the second aspect. In another possible design, thedecoder in the second aspect may be a part of the processor.

Optionally, the communications apparatus may further include atransceiver and an antenna.

Optionally, the communications apparatus may further include a componentconfigured to generate a transport block cyclical redundancy check(CRC), a component used for code block segmentation and CRC check, aninterleaver used for interleaving, a modulator used for modulationprocessing, or the like.

Optionally, the communications apparatus may further include ademodulator used for demodulation, a de-interleaver used forde-interleaving, a component used for de-rate matching, or the like.Functions of these components may be implemented by the one or moreprocessors.

In a possible design, functions of these components may be implementedby the one or more processors.

According to a sixth aspect, an embodiment of the present applicationprovides a communications system, and the system includes thecommunications apparatus described in the third aspect and thecommunications apparatus described in the fourth aspect.

According to a seventh aspect, an embodiment of the present applicationprovides a communications system, and the system includes one or morecommunications apparatuses described in the fifth aspect.

According to another aspect, an embodiment of the present applicationprovides a computer storage medium, where the computer storage mediumstores a program, and when the program is run, a computer is caused toperform the methods described in the foregoing aspects.

According to another aspect of this application, a computer programproduct including an instruction is provided. When the instruction isrun on a computer, the computer is caused to perform the methods in theforegoing aspects.

According to the information processing method, the apparatus, thecommunications device, and the communications system in the embodimentsof the present application, flexible code length and code raterequirements of the communication system can be met in terms of encodingperformance and error floor.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows schematic diagrams of a base graph, a base matrix, andcircular permutation matrices of an LDPC code;

FIG. 2 is a schematic structural diagram of a base graph of an LDPCcode;

FIG. 3 a is a schematic diagram of a base graph of an LDPC codeaccording to an embodiment of the present application;

FIG. 3 b -1 and FIG. 3 b -2 show schematic diagrams of base matrices ofan LDPC code according to an embodiment of the present application;

FIG. 3 c -1 to FIG. 3 c -11 show schematic diagrams of base matrices ofLDPC code according to another embodiment of the present application;

FIG. 4 is a schematic performance diagram provided by an embodiment ofthe present application;

FIG. 5 is a schematic performance diagram provided by another embodimentof the present application;

FIG. 6 is a block diagram of an information processing apparatusaccording to an embodiment of the present application;

FIG. 7 is a block diagram of a communications system according to anembodiment of the present application;

FIG. 8 a is a schematic diagram of a base graph of an LDPC codeaccording to another embodiment of the present application;

FIG. 8 b -1 and FIG. 8 b -2 show schematic diagrams of base matrices ofan LDPC code according to yet another embodiment of the presentapplication;

FIG. 8 c -1 to FIG. 8 c -10 show schematic diagrams of base matrices ofLDPC code according to still another embodiment of the presentapplication;

FIG. 9 is a schematic performance diagram of an LDPC code according toan embodiment of the present application;

FIG. 10 is a schematic performance diagram of an LDPC code according toanother embodiment of the present application;

FIG. 11 a is a schematic diagram of a base graph of an LDPC codeaccording to yet another embodiment of the present application;

FIG. 11 b is a schematic diagram of a base matrix based on the basegraph of the LDPC code provided in FIG. 11 a ; and

FIG. 12 is a schematic diagram of a base graph according to stillanother embodiment of the present application.

DETAILED DESCRIPTION OF EMBODIMENTS

For ease of understanding, some terms used in this application aredescribed below.

In this application, terms “network” and “system” are ofteninterchangeably used, and “apparatus” and “device” are also ofteninterchangeably used. A “communication apparatus” may refer to a chip(such as a baseband chip, a digital signal processing chip, or ageneral-purpose chip), a terminal, a base station, or any othernetworking device.

A terminal is a device having a communication function. It may be ahandheld device, an in-vehicle device, a wearable device, a computingdevice, or any other processing device that is connected to a wirelessmodem and having wireless communication functions. The terminal may becalled by different names in different networks, such as user equipment,mobile station, subscriber unit, station, cellular phone, personaldigital assistant, wireless modem, wireless communications device,handheld device, laptop computer, cordless phone, and wireless localloop station. For ease of description, these devices are simply referredto as a “terminal” in this application.

A base station (BS) may also be referred to as a base station device,and is a device deployed in a radio access network to provide wirelesscommunication functions. The base station may be called by differentnames in different wireless access systems. For example, a base stationin a Universal Mobile Telecommunications System (UMTS) network isreferred to as a NodeB, a base station in an LTE network is referred toas an evolved NodeB (eNB or eNodeB), a base station in a new radio (NR)network is referred to as a transmission reception point (TRP) or a nextgeneration NodeB (gNB). Base stations in other networks may be called byother names. This is not limited in the present application.

The following describes the technical solutions in the embodiments ofthe present application with reference to the accompanying drawings.

An LDPC code can be represented by a parity-check matrix H. Theparity-check matrix H code can be obtained by using a base graph and ashift value. The base graph is a matrix of m rows and n columns andincludes m*n matrix elements (also called entries). Symbol * meansmultiply hereinafter. Value of each matrix element is either 0 or 1. Anelement whose value is 0 is referred to as a zero-element, which may bereplaced by an all-zero matrix of Z rows and Z columns. An element whosevalue is 1 is referred to as a non-zero-element, which may be replacedby a circular permutation matrix of Z rows and Z columns. In both cases,Z is a positive integer. In other words, each element of the base graphrepresents one all-zero matrix or one circular permutation matrix. FIG.1 shows an example 10 a of a base graph of an LDPC code with QCstructure, in which elements are either 0 or 1, where m=4, and n=20.

It should be noted that, in this application, row indexes and columnindexes of base graphs and base matrices are numbered starting from 0,and this is merely for ease of description. For example, column 0indicates a first column in a base graph or a base matrix, and column 1indicates a second column in the base graph or the base matrix, row 0indicates a first row in the base graph or the base matrix, row 1indicates a second row in the base graph or the base matrix, and so on.

It is understood that row indexes and column indexes may alternativelybe numbered from 1, or any number.

If a value of an element in row i and column j (i and j are respectivelyrow and column indexes as defined above, i.e. starting from 0) in thebase graph is 1 (i.e. it is a non-zero-element), it is assigned a shiftvalue P_(i,j). P_(i,j) is an integer greater than or equal to 0. Inconstructing a parity-check matrix H of the LDPC code, thenon-zero-element in the row i and the column j of the base graph isreplaced by a Z*Z circular permutation matrix corresponding to P_(i,j).The circular permutation matrix corresponding to P_(i,j) equals to amatrix obtained by performing a right cyclic shift for P_(i,j) times ona Z*Z identity matrix. Each element in the base graph whose value is 0(i.e. it is a zero-element) is replaced by a Z*Z all-zero matrix. Shiftvalues P_(i,j) may be indicated in the base graph as shown in 10 b ofFIG. 1 . A non-zero-element in the base graph 10 a corresponds to ashift value in 10 b at the same column and same row.

Z is a lifting factor, or sometimes be referred to as a lifting size. Zmay be determined based on code block sizes that are supported by asystem and size of information data. It can be seen that for a basegraph of m rows * n columns, the parity-check matrix H has a size of(m*Z)*(n*Z). For example, if the lifting factor Z is 4, eachzero-element in the base graph 10 a is replaced by one 4*4 all-zeromatrix 11 a. If P_(2,3) is 2, a non-zero-element in row 2 and column 3in the base graph is replaced by a 4*4 circular permutation matrix 11 d,and the matrix 11 d is obtained by performing a right cyclic shift on a4*4 identity matrix 11 b twice. If P_(2,4) is 0, a non-zero-element inrow 2 and column 4 is replaced by the identity matrix 11 b. It should benoted that only examples are described herein, and the examples do notconstitute a limitation.

Value of P_(i,j) may depend on the lifting factor Z. For a non-zeroelement of the base graph at row i, column j, P_(i,j) may be differentfor different lifting factors Z. For ease of implementation, an m*n basematrix may be defined. Elements in the base matrix are in a one-to-onecorrespondence with elements in the base graph. A zero-element in thebase graph has a same position in the base matrix, and the element isindicated by a value −1. A non-zero-element in row i and column j, whosevalue is 1 in the base graph, has a same position in the base matrix.The non-zero element is indicated by a shift value P_(i,j). P_(i,j) is apositive integer greater than or equal to 0. In the embodiments of theapplication, sometimes the base matrix is also referred to as a shiftmatrix of the base graph.

FIG. 1 shows a base matrix 10 b corresponding to the base graph 10 a.

Normally, the base graph or the base matrix of the LDPC code may furtherinclude p columns of built-in puncture bits, where p may be 1 or 2.These columns may be used in encoding, but system bits corresponding tothe encoding using these columns are not sent. A code rate of the basematrix of the LDPC code meets R=(n−m)/(n−p). If a base matrix of fourrows and 20 columns (4*20), includes two columns of built-in puncturebits, a code rate is (20−4)/(20−2)=8/9.

An LDPC code used in a wireless communication system is a QC-LDPC code,and parity bits part in a base graph of the QC-LDPC code has abi-diagonal structure or a raptor-like structure, so that encoding canbe simplified and incremental redundancy hybrid repeat can be supported.In a decoder for the QC-LDPC code, a QC-LDPC shift network (QSN), aBanyan network, or a Benes network is usually used to implement a cyclicshift of information.

A base graph of the QC-LDPC code with the raptor-like structure is amatrix of m rows and n columns, and the base graph may include fivesubmatrices: A, B, C, D, and E. A weight of the matrix is determined bya quantity of non-zero-elements in the matrix. A row weight of a row isa quantity of non-zero-elements in the row, and a column weight of acolumn is a quantity of non-zero-elements in the column.

As shown in FIG. 2 , submatrix A is a matrix of m_(A) rows and n_(A)columns, and the submatrix A has a size of m_(A)*n_(A). Each columncorresponds to Z system bits in the LDPC code, and a system bit issometimes referred to as an information bit.

Submatrix B is a square matrix of m_(A) rows and m_(A) columns, and thesubmatrix B has a size of m_(A)*m_(A). Each column corresponds to Zparity bits in the LDPC code. As shown in 20 a of FIG. 2 , the submatrixB includes a submatrix B′ with a bi-diagonal structure, and a matrixcolumn whose weight is 3 (weight-3 column for short), and the weight-3column is located at the left side of the submatrix B′. As shown in 20 bor 20 c of FIG. 2 , the submatrix B may further include a matrix columnwhose weight is 1 (weight-1 matrix column for short), the weight-1matrix column may be located in a first or last column in the submatrixB. A non-zero-element in the weight-1 matrix column is in a last row inthe submatrix B, so that a weight of the last row in the submatrix B is1.

Generally, a matrix generated based on the submatrix A and the submatrixB is a core matrix, which may be used to support high code-rateencoding.

Continuing in FIG. 2 , Submatrix C is an all-zero matrix, and thesubmatrix C has a size of m_(A)*(n−(m_(A)−n_(A))). Submatrix E is anidentity matrix, and the submatrix E has a size of (m−m_(A))*(m−m_(A)).Submatrix D has a size of (m−m_(A))*(n_(A)+m_(A)), and the submatrix Dmay be used to generate low bit-rate parity bits.

It may be understood that, the base graph is expressed mathematically,and because submatrix C is an all-zero matrix, and submatrix E is anidentity matrix, in a possible implementation, a matrix including thesubmatrix A and the submatrix B, or a matrix including the submatrix A,the submatrix B, and the submatrix D may be used to represent a basegraph of a matrix in encoding or decoding.

Because structures of the submatrix B, the submatrix C, and thesubmatrix E are relatively fixed, structures of the submatrix A and thesubmatrix D are determining factors affecting encoding and decodingperformance of the LDPC code.

When an LDPC matrix with the raptor-like structure is used for encoding,in a possible implementation, the part of the matrix including thesubmatrix A and the submatrix B, namely the core matrix, may be firstencoded to obtain one or more parity bits corresponding to the submatrixB. Then, the entire matrix is encoded to obtain one or more parity bitscorresponding to the submatrix E. Because the submatrix B may includethe submatrix B′ with the bi-diagonal structure and the weight-1 matrixcolumn, during the encoding, one or more parity bits corresponding tothe bi-diagonal structure may be first obtained, and then one or moreparity bits corresponding to the weight-1 matrix column may be obtained.

The following provides an example of encoding method. Assuming that thecore matrix including the submatrix A and the submatrix B is H_(core), aweight-1 matrix column and a row in which a non-zero-element in thecolumn is located are removed from the H_(core) to obtain a matrixH_(core-dual). One or more parity bits in the H_(core-dual) isrepresented by H_(e)[H_(e1) H_(e2)], H_(e1) is a weight-3 matrix column,and H_(e2) has a bi-diagonal structure. According to a defined LDPC codematrix, H_(core-dual)·[S P_(e)]^(T)=0, where S is an input sequence andis a vector including information bits, P_(e) is a vector includingparity bits, and [S P_(e)]^(T) indicates a transposed matrix includingthe input sequence S and P_(e). Therefore, the parity bit correspondingto H_(core-dual) may be first calculated based on the input sequence Sand H_(core-dual), where the input sequence S includes all informationbits. Then, one or more parity bits corresponding to the weight-1 matrixcolumn in the submatrix B is calculated based on the obtained parity bitcorresponding to H_(core-dual) and the input sequence S. In this case,all parity bits corresponding to the submatrix B may be obtained. Afterthat, one or more parity bits corresponding to the submatrix E isobtained by encoding using the submatrix D and based on the inputsequence S and the parity bits corresponding to the submatrix B, toobtain all information bits and all parity bits. These bits form asequence obtained by encoding, namely, an LDPC code sequence.

Optionally, LDPC encoding may further include a shortening operation anda puncturing operation. The shortened bits and the punctured bits arenot sent.

The shortening is usually performed starting from a last informationbit, and may be performed in different manners. For example, if aquantity of shortened bits is s₀, the last s₀ bits in the input sequenceS may be set to known bits, such as set to 0 or null or another value,to obtain an input sequence S′, and then the input sequence S′ isencoded by using an LDPC matrix. For another example, the last (s₀ modZ) bits in the input sequence S may be set to known bits, such as set to0 or null or another value, to obtain an input sequence S′, and the last

$\left\lfloor \frac{s_{0}}{Z} \right\rfloor$columns in the submatrix A are deleted to obtain an LDPC matrix H′, andthe input sequence S′ is encoded by using the LDPC matrix H′, or thelast

$\left\lfloor \frac{s_{0}}{Z} \right\rfloor$columns in the submatrix A do not participate in encoding of the inputsequence S′. After the encoding, the shortened bits are not sent.

The puncturing may be performed on one or more built-in puncture bits,or, one or more parity bits in an input sequence. Usually puncturing oneor more parity bits is also from the last one bit in parity bits.Alternatively, puncturing may be performed based on a preset puncturingpattern in the system. In a possible implementation, an input sequenceis first encoded, and then based on a quantity p of bits that need to bepunctured, the last p bit(s) in parity bits are selected or p bit(s) areselected based on the preset puncturing pattern in the system, where thep bit(s) are not sent. In another possible implementation, p column(s)in a matrix that correspond to punctured bits and p row(s) in whichnon-zero-elements in these columns are located may also be determined,and the rows and the columns are not used in encoding, and therefore, nocorresponding parity bits are generated.

It should be noted that the encoding implementation described herein ismerely used as an example. Other known encoding implementations may beused based on the base graph and/or the base matrix provided in thisapplication, and the encoding implementations are not limited in thisapplication. Decoding in this application may be performed in aplurality of decoding methods, for example, a min-sum (MS) decodingmethod or a belief propagation decoding method. The MS decoding methodis sometimes referred to as a flood MS decoding method. For example, aninput sequence is initialized and one or more iterations are performed.Hard decision detection is performed after the iteration(s), and a harddecision result is checked. If the decoding result meets a checkequation, decoding succeeds, an iteration ends, and a decision result isoutput. If a decoding result does not meet a check equation, aniteration is performed again within a maximum quantity of iterationtimes, and if check still fails when the maximum quantity of iterationtimes is reached, decoding fails. The principle of the MS decoding isknown, and details are not described herein.

It should be noted that the decoding method is merely used as an exampleherein, other decoding methods may be used based on the base graphand/or the base matrix provided in this application, and the decodingmethod is not limited in this application.

An LDPC code may be obtained based on a base graph and a base matrix, aperformance upper limit of the LDPC code may be determined by performingdensity evolution on the base graph or the base matrix. An error floorof the LDPC code is determined based on a shift value in the basematrix. Improving encoding and decoding performance and lowering theerror floor are some of objectives of designing the base graph and thebase matrix. In wireless communication systems, code lengths are widelyvaried. A code block may have a short block length such as 40 bits or1280 bits, or a code block may have a long block length such as 5000bits or 8448 bits. FIG. 3 a , FIGS. 3 b -1 and 3 b-2, and FIGS. 3 c -1to 3 c-11 are examples of a base graph and base matrices of an LDPCcode, and these examples can meet a performance requirement of a codeblock having a block length of up to 8448 bits.

Additionally, FIG. 8 a , FIGS. 8 b -1 and 8 b-2, and FIGS. 8 c -1 to 8c-10 provide examples of a base graph and base matrices of another LDPCcode. FIG. 11 a and FIG. 11 b provide examples of a base graph and abase matrix of yet another LDPC code.

For ease of description and understanding, row indexes and columnindexes are respectively shown on the uppermost side and the leftmostside in FIG. 3 a , FIGS. 3 b -1 and 3 b-2, FIGS. 3 c -1 to 3 c-11, FIG.8 a , FIGS. 8 b -1 and 8 b-2, FIGS. 8 c -1 to 8 c-10, FIG. 11 a and FIG.11 b . For example, FIG. 3 a shows a base graph 30 a of an LDPC code.The base graph has 46 rows and 68 columns. In the figure, 0 to 67 in theuppermost row indicate column indexes, and 0 to 45 in the leftmostcolumn indicate row indexes. Shown in FIG. 4 and FIG. 5 are performancediagrams of the LDPC code shown in FIG. 3 a , FIGS. 3 b -1 and 3 b-2,and FIGS. 3 c -1 to 3 c-11 at two different code rates.

In the base graph 30 a, submatrix A corresponds to system bits, has fiverows and 22 columns, and includes elements in row 0 to row 4 and column0 to column 21. Submatrix B corresponds to parity bits, has five rowsand five columns, and includes elements in the row 0 to the row 4 andcolumn 22 to column 26.

The submatrix A and the submatrix B form a core matrix in the base graph30 a of the LDPC code, and to be specific, form a matrix of five rowsand 27 columns, and may be used for high bit-rate encoding. For example,in the core matrix including the submatrix A and the submatrix B, onecolumn has a weight of 5, one column has a weight of 4, 21 columns havea weight of 3, three columns have a weight of 2, and one column has aweight of 1.

The submatrix A may include two columns of built-in puncture bits, andafter puncturing, a code rate that can be supported by the core matrixis 22/(27−2)=0.88. In the submatrix A, one column has a weight of 5, onecolumn has a weight of 4, and other 20 columns have a weight of 3. Forexample, weights of the two columns of built-in puncture bits may berespectively 5 and 4.

Both a weight of a last row (row 4) and a weight of a last column(column 4 in the submatrix B, that is, column 26 in the core matrix) inthe submatrix B are 1. The submatrix B includes one weight-3 column, andto be specific, a weight of column 0 in the submatrix B (column 22 inthe core matrix) is 3. Column 1 to column 3 in the submatrix B (column23 to column 25 in the core matrix) and row 0 to row 3 in the submatrixB form a bi-diagonal structure.

The core matrix in the base graph 30 a includes four rows whose weightsare 19 and one row whose weight is 3. Weights of the rows in the corematrix including the submatrix A and the submatrix B are 19, 19, 19, 19,and 3. It should be noted that the rows in the core matrix may beswitched, for example, row 0 and row 2 are switched with each other, androw 1 and row 3 are switched with each other. The row whose weight is 3may be row 4 in column 0 to column 26 in the core matrix in the basegraph 30 a, and the rows whose weights are 19 may be respectively row 0to row 3 in column 0 to column 26 in the core matrix in the base graph30 a. These rows may be switched with each other, and the columns mayalso be switched with each other. For example, column 8 and column 25 inthe core matrix may be switched with each other, and column 10 andcolumn 26 may be switched with each other. For example, row 3 and row 0in the core matrix may be switched with each other, and row 2 and row 1may be switched with each other. To maintain the bi-diagonal structurein the submatrix B, on this basis, column 23 and column 25 may beswitched with each other to obtain a core matrix in a base graph 80 ashown in FIG. 8 a , that is, a matrix including row 0 to row 5 andcolumn 0 to column 26 in 80 a. It should be noted that, only examplesare provided herein. In an actual application, row permutation andcolumn permutation may be flexibly designed based on a systemrequirement.

Table 1 shows an example of column permutation for the base graph 80 a.For ease of description, a sequence, obtained by column permutation, of27 columns in the core matrix is provided herein. Column indexes arecolumn indexes of the matrix after the permutation, and are numberedfrom 0. Column indexes before the permutation are column indexes of thematrix before the permutation. As shown in Table 1, column 8 and column10 in the matrix before the permutation are switched to column 25 andcolumn 26, column 9 in the matrix before the permutation is switched tocolumn 8, column 11 to column 21 in the matrix before the permutationare switched to column 9 to column 19, and column 25 and column 26 inthe matrix before the permutation are switched to column 20 and column21. In this manner, performance of a specific code rate and a specificcode length may be improved.

FIG. 9 is a performance diagram based on the base matrix shown inTable 1. Performance is improved in a case of a code rate of 2/3, ablock error rate (BLER) of 1E-2, and a code length ranging from 672 to960.

FIG. 10 is another performance diagram based on the base matrix shown inTable 1. Performance is improved in a case of a code rate of 2/3, a BLERof 1E-2, and a code length ranging from 1952 to 2624.

TABLE 1 Column index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Column index 0 1 23 4 5 6 7 9 11 12 13 14 15 before permutation Column index 14 15 16 1718 19 20 21 22 23 24 25 26 Column index 16 17 18 19 20 21 25 26 22 23 248 10 before permutation

It may be understood that because in a matrix, rows may be switched witheach other, columns may also be switched with each other, rowpermutation does not change weights of the columns in the matrix, columnpermutation does not change weights of the rows in the matrix, and aquantity of non-zero-elements in the matrix is unchanged. The weights ofthe rows in the base graph 80 a after row permutation and columnpermutation are unchanged. Performance is not affected for a base graphobtained by performing row permutation, or column permutation, or rowpermutation and column permutation.

It should be noted that in this application, that performance is notaffected means that impact is acceptable and falls within a tolerablerange as a whole. For example, performance is little affected as a wholebecause performance deteriorates in an allowable range in some scenariosor in some ranges, but performance is improved in some scenarios or insome ranges.

The core matrix in the base graph 30 a and that in the base graph 80 aare used as examples. After row permutation is performed on the basegraph 30 a, the core matrix in the base graph 80 a still includes thecolumns in the core matrix in the base graph 30 a, one row has a weightof 3, and other four rows have a weight of 19, except that the order ofthe rows changes. If column permutation is performed on the base graph30 a, for example, column 5 and column 7 are switched with each other,it can be found that a core matrix that is of the base graph 30 a andthat is obtained by performing the column permutation still includes thecolumns in the core matrix in the base graph 30 a. One column has aweight of 5, one column has a weight of 4, 21 columns have a weight of3, three columns have a weight of 2, and one column has a weight of 1,except that the order of the columns changes. It should be noted thatprovided herein are only examples, and the examples do not constitute alimitation.

For a given base graph or a given base matrix of an LDPC code, impact ofa few changes to matrix elements on performance is usually acceptable.For example, in an implementation, a few changes may be made based onthe core matrix in the base graph 30 a. For example, one row has aweight of greater than or equal to 1 and less than or equal to 5, andother four rows have weights greater than or equal to 17 and less thanor equal to 21, respectively. For example, one row has a weight of 2,and other four rows have a weight of 18; or one row has a weight of 4,and other four rows respectively have weights of 17, 18, 19, and 19. Itmay be understood that, weights of some rows may be increased ordecreased by 1 or 2 with reference to the solutions provided in thisapplication, and this is not limited in this application.

The submatrix A may also include one row, in which elements other thanelements in the columns of built-in puncture bits are zero-elements.Further, to minimize a weight of the row in the core matrix or the basegraph matrix, the row is usually the same as a row whose weight is 1 inthe submatrix B. For example, there are two columns of built-in puncturebits, and to be specific, column 0 and column 1 are columns of built-inpuncture bits, as shown in the base graph 30 a or 80 a. In row 4,elements in column 0 and column 1 are non-zero-elements, elements incolumn 2 to column 25 are zero-elements, elements in column 26 arenon-zero-elements, and a weight of row 4 is 3. Row 4 has a smallestweight in the core matrix, and even in the entire base graph matrix.Such setting can improve encoding and decoding performance.

To support different block lengths, the LDPC code needs differentlifting factors Z. For example, the lifting factor Z may be one or moreof the following values: 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44,48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112, 120, 128, 144, 160, 176,192, 208, 224, 240, 256, 288, 320, 352, or 384. To ensure LDPC codeperformance in cases of different block lengths, base matricescorresponding to different lifting factors Z may be used based on thedifferent lifting factors Z. FIG. 3 b -1 and FIG. 3 b -2 show aplurality of base matrix examples of the core matrix in the base graph30 a. Base matrices are obtained based on the core matrix in the basegraph 30 a and the lifting factor Z. A non-zero-element in row i andcolumn j in the base graph 30 a has a shift value P_(i,j) in row i andcolumn j in the base matrix, and a zero-element in the base graph 30 ais represented by −1 or null in the base matrix.

In a possible implementation, one of the following may be selected:

if the lifting factor Z is one of {16, 18, 20, 22, 24, 26, 28, 30}, apart that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be shown in abase matrix 30 b-1 in FIG. 3 b -1; or

if the lifting factor Z is one of {32, 36, 40, 44, 48, 52, 56, 60}, apart that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be shown in abase matrix 30 b-2 in FIG. 3 b -1; or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be shown in abase matrix 30 b-3 in FIG. 3 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be shown in abase matrix 30 b-4 in FIG. 3 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in a base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be shown in a base matrix 30 b-5 inFIG. 3 b -1.

In another possible implementation, a lifting factor set may be {24, 26,28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112,120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384},and one of the following may be selected:

if the lifting factor Z is one of {24, 26, 28, 30}, a part that is in abase matrix of the base graph 30 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 30 b-6 shown in FIG. 3 b -2;or

if the lifting factor Z is one of {32, 36, 40, 44}, a part that is in abase matrix of the base graph 30 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 30 b-7 shown in FIG. 3 b -2;or

if the lifting factor Z is one of {48, 52, 56, 60}, a part that is in abase matrix of the base graph 30 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 30 b-8 shown in FIG. 3 b -2;or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrix30 b-3 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in a base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrixshown in 30 b-4 in FIG. 3 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in a base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-5 shown inFIG. 3 b -1.

Based on the foregoing implementations, in another possibleimplementation, to further improve performance, the base graph maycorrespond to more base matrices, and parts that are in the basematrices of the base graph 30 a and that correspond to the submatrix Aand the submatrix B may correspond to different base matrices. Forexample,

if the lifting factor Z is one of {24, 26, 28, 30}, a part that is inthe base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-6 shown inFIG. 3 b -2; or

if the lifting factor Z is one of {32, 36, 40, 44}, a part that is inthe base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-7 shown inFIG. 3 b -2; or

if the lifting factor Z is one of {48, 52, 56, 60}, a part that is inthe base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-8 shown inFIG. 3 b -2; or

if the lifting factor Z is one of {64, 72, 80, 88}, a part that is inthe base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-9 or 30 b-10shown in FIG. 3 b -2; or

if the lifting factor Z is one of {96, 104, 112, 120}, a part that is inthe base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-3 shown inFIG. 3 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in the base matrix of the base graph 30 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrix30 b-4 shown in FIG. 3 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in the base matrix of the base graph 30 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 30 b-5 shown inFIG. 3 b -1.

FIG. 8 b shows a plurality of base matrix examples of the core matrix inthe base graph 80 a. Base matrices are obtained based on the core matrixin the base graph 80 a and the lifting factor Z. A non-zero-element inrow i and column j in the base graph 80 a has a shift value P_(i,j) inrow i and column j in the base matrix, and a zero-element in the basegraph 80 a is represented by −1 or null in a shift matrix.

In another possible implementation, a lifting factor set may be {24, 26,28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112,120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384},and one of the following may be selected:

if the lifting factor Z is one of {24, 26, 28, 30}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 80 b-1 shown in FIG. 8 b -1;or

if the lifting factor Z is one of {32, 36, 40, 44}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 80 b-2 shown in FIG. 8 b -1;or

if the lifting factor Z is one of {48, 52, 56, 60}, a part that is in abase matrix of the base graph 80 a and that corresponds to the submatrixA and the submatrix B may be a base matrix 80 b-3 shown in FIG. 8 b -1;or

if the lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112,120}, a part that is in a base matrix of the base graph 80 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrix80 b-4 shown in FIG. 8 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in a base matrix of the base graph 80 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrix80 b-5 shown in FIG. 8 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in a base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-6 shown inFIG. 8 b -2.

Based on the foregoing implementation, in another possibleimplementation, to further improve performance, the base graph maycorrespond to more base matrices, and parts that are in the basematrices of the base graph 80 a and that correspond to the submatrix Aand the submatrix B may correspond to different base matrices. Forexample,

if the lifting factor Z is one of {24, 26, 28, 30}, a part that is inthe base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-1 shown inFIG. 8 b -1; or

if the lifting factor Z is one of {32, 36, 40, 44}, a part that is inthe base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-2 shown inFIG. 8 b -1; or

if the lifting factor Z is one of {48, 52, 56, 60}, a part that is inthe base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-3 shown inFIG. 8 b -1; or

if the lifting factor Z is one of {64, 72, 80, 88}, a part that is inthe base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-7 or 80 b-8shown in FIG. 8 b -2; or

if the lifting factor Z is one of {96, 104, 112, 120}, a part that is inthe base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-4 shown inFIG. 8 b -1; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, a part that is in the base matrix of the base graph 80 a and thatcorresponds to the submatrix A and the submatrix B may be a base matrix80 b-5 shown in FIG. 8 b -1; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, a part thatis in the base matrix of the base graph 80 a and that corresponds to thesubmatrix A and the submatrix B may be a base matrix 80 b-6 shown inFIG. 8 b -2.

In another possible implementation, a part that is in a base matrix ofthe base graph 80 a and that corresponds to the submatrix A and thesubmatrix B may be a base matrix 80 b-9 shown in FIG. 8 b -2. Becauselifting factors Z may be classified in a plurality of manners, a basematrix used for a group of lifting factors Z may be considered in termsof performance accordingly.

For example, a value of the lifting factor Z is determined based on alength K of the input sequence. For example, if the length of the inputsequence is K, a minimum value that meets 22*Z≥K may be determined froma plurality of lifting factors defined in the system and may be used asthe value of the lifting factor of the matrix. Further, a correspondingbase matrix may be selected based on the determined lifting factor.Table 2 shows an example of a correspondence between a base matrix and alifting factor. A plurality of lifting factors defined in the system areclassified into eight groups, that is, eight sets, and set indexes are 1to 8. Correspondingly, there are eight base matrices PCM1 to PCM 8 (PCMstands for parity-check matrix).

TABLE 2 Base matrix index Lifting factor Z PCM 1 2 4 8 16 32 64 128 256PCM 2 3 6 12 24 48 96 192 384 PCM 3 5 10 20 40 80 160 320 PCM 4 7 14 2856 112 224 PCM 5 9 18 36 72 144 288 PCM 6 11 22 44 88 176 352 PCM 7 1326 52 104 208 PCM 8 15 30 60 120 240

For example, the base matrix 80 b-9 may be used as PCM 8, and in thiscase, when the lifting factor Z is any one of 15, 30, 60, 120, or 240,80 b-9 may be used as a base matrix, and correspondingly, the basematrix is lifted by using the lifting factor Z to obtain an LDPCparity-check matrix. Further, when Z is greater than or equal to 24, thebase matrix 80 b-9 has relatively high performance.

Likewise, rows may be switched with each other, and columns may also beswitched with each other in a base matrix. If at least one of rowpermutation or column permutation is performed on a base graph, samepermutation is also performed on a corresponding base matrix.

It can be learned that, in the foregoing implementations, 80 b-1 is abase matrix obtained by performing row permutation and columnpermutation on base matrix 30 b-6. 80 b-2 is a base matrix obtained byperforming row permutation and column permutation on base matrix 30 b-7.80 b-3 is a base matrix obtained by performing row permutation andcolumn permutation on base matrix 30 b-8. 80 b-4 is a base matrixobtained by performing row permutation and column permutation on basematrix 30 b-3. 80 b-5 is a base matrix obtained by performing rowpermutation and column permutation on base matrix 30 b-4. 80 b-6 is abase matrix obtained by performing row permutation and columnpermutation on base matrix 30 b-5. 80 b-7 is a base matrix obtained byperforming row permutation and column permutation on base matrix 30 b-9.80 b-8 is a base matrix obtained by performing row permutation andcolumn permutation on base matrix 30 b-10.

Certainly, it may be understood that the part that is in the base matrixof the LDPC matrix and that corresponds to the submatrix A and thesubmatrix B may include rows or columns in any one of the base matrices30 b-1, 30 b-2, 30 b-3, 30 b-4, 30 b-5, 30 b-6, 30 b-7, 30 b-8, 30 b-9,or 30 b-10. In other words, the matrix may be obtained by performingcolumn permutation, or row permutation, or row permutation and columnpermutation on any one of the base matrices 30 b-1, 30 b-2, 30 b-3, 30b-4, 30 b-5, 30 b-6, 30 b-7, 30 b-8, 30 b-9, or 30 b-10.

To obtain a flexible code rate, a submatrix C, a submatrix D, and asubmatrix E of corresponding sizes may be added based on a core matrix,to obtain different code rates. Because the submatrix C is an all-zeromatrix, and the submatrix E is an identity matrix, sizes of thesubmatrix C and the submatrix E are determined based on code rates, andstructures of the submatrix C and the submatrix E are relatively fixed.Mainly the core matrix and the submatrix D affect encoding and decodingperformance. Rows and columns are added based on the core matrix to formcorresponding C, D, and E, so that different code rates can be obtained.For example, the core matrix in the base graph 30 a or the core matrixin the base graph 80 a may be used as the core matrix, and thecorresponding submatrices C, D, and E are added to meet encoding ordecoding requirements for different code rates.

A column count of the submatrix D is a sum of column counts of asubmatrix A and a submatrix B, and a row count of the submatrix D ismainly related to a code rate. The base graph 30 a is used as anexample. A column count m_(D) of the corresponding submatrix D is(n_(A)+m_(A))=27 columns. If a code rate supported by an LDPC code isR_(m), sizes of a base graph or a base matrix of the LDPC code are m*n,where n=n_(A)/R_(m)+p, and m=n−n_(A)=n_(A)/R_(m)+p−n_(A). If the minimumcode rate R_(m) is 1/3, and a quantity p of columns of built-in puncturebits is 2, in the example of the base graph 30 a, n=68, m=46, a rowcount m_(D) of the submatrix D may be up to m−m_(A)=46−5=41, and0≤m_(D)≤41.

For ease of description, a matrix F of 41 rows and 27 columns may bedefined. In this case, the submatrix D may include m_(D) rows in thematrix F, and the submatrix D, the submatrix A, the submatrix B, and thesubmatrix C and the submatrix E of corresponding sizes form a base graphthat is of an LDPC code whose code rate is 22/(25+m_(D)). In the basegraph 30 a, m_(D)=41, and the submatrix D has 41 rows and 27 columnscorrespondingly. To be specific, the submatrix D is the matrix F, and acorresponding code rate supported by the LDPC code is 22/66=1/3. It canbe learned that a matrix including row 5 to row 45 and column 0 tocolumn 26 in the base graph 30 a is the matrix F.

Row weights of the matrix F shown in base graph 30 a as an example aresequentially 7, 7, 9, 8, 7, 7, 8, 6, 6, 5, 6, 5, 5, 6, 5, 5, 5, 5, 4, 4,4, 5, 4, 5, 4, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 3, 3, and 4.

Because the submatrix E is an identity matrix, weights of rows in thebase graph 30 a are 8, 8, 10, 9, 8, 8, 9, 7, 7, 6, 7, 6, 6, 7, 6, 6, 6,6, 5, 5, 5, 6, 5, 6, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 4, 5, 5, 4, 4, 4, and5.

In the present application, if there is at most one non-zero-element intwo adjacent rows in a same column in a base graph, the two rows aremutually orthogonal.

In a possible implementation, the matrix F may be a matrix with aquasi-orthogonal structure. In a matrix block including columns otherthan columns of built-in puncture bits in the matrix F, there is amaximum of only one non-zero-element in any two adjacent rows in a samecolumn, that is, the matrix block including the columns other than thecolumns of built-in puncture bits in the matrix F has an orthogonalstructure. In the example of the base graph 30 a, the matrix F is amatrix including row 5 to row 45 and column 0 to column 26, and column 0and column 1 are columns of built-in puncture bits. In a matrix blockincluding row 5 to row 45 and column 2 to column 26, row 5 and row 6 aremutually orthogonal, row 6 and row 7 are mutually orthogonal, row 23 androw 24 are mutually orthogonal, row 32 and row 33 are mutuallyorthogonal, and so on. If m_(D)=15, the submatrix D in the base graph ofthe LDPC code has 15 rows and 27 columns. The submatrix D may be amatrix including row 0 to row 14 in the matrix F in the base graph 30 a,that is, row 5 to row 19 in the base graph 30 a, and column 0 to column26. A corresponding code rate supported by the LDPC code is 22/40=0.55.At this code rate, the base graph of the LDPC code corresponds to amatrix including row 0 to row 19 and column 0 to column 41 in the basegraph 30 a. The submatrix E is an identity matrix of 15 rows and 15columns, and the submatrix C is an all-zero matrix of 5 rows and 15columns.

If m_(D)=19, the submatrix D in the base graph of the LDPC code has 19rows and 27 columns. The submatrix D may be a matrix including row 0 torow 18 in the matrix F in the base graph 30 a, that is, row 5 to row 23in the base graph 30 a, and column 0 to column 26. A corresponding coderate supported by the LDPC code is 22/44=1/2. At this code rate, thebase graph of the LDPC code corresponds to a matrix including row 0 torow 23 and column 0 to column 41 in the base graph 30 a. The submatrix Eis an identity matrix of 19 rows and 19 columns, and the submatrix C isan all-zero matrix of five rows and 19 columns.

The same is true if m_(D) is another value, and details are notdescribed.

It should be noted that rows may be switched with each other, andcolumns may also be switched with each other in the base graph and thebase matrix of the LDPC code. For example, row 17 and row 19 in the basegraph 30 a may be switched with each other, and column 39 and column 41may be switched with each other, to obtain the base graph matrix 80 ashown in FIG. 8 a.

For another example, the submatrix D includes m_(D) rows in the matrixF, row permutation may not be performed between the m_(D) rows, or rowpermutation may be performed between one or more of the m_(D) rows; andthe submatrix E still has a diagonal structure, and no row permutationor column permutation is performed on the submatrix E.

For example, row 12 and row 14 in the matrix F are switched with eachother, the submatrix D includes m_(D) rows in the submatrix F, and thesubmatrix E still has a diagonal structure, to obtain the base graph 80a. The matrix F is a quasi-orthogonal matrix before the row permutation,and the matrix F is still a quasi-orthogonal matrix after thepermutation.

For example, in the base graph 80 a, the matrix F is a matrix includingrow 5 to row 45 and column 0 to column 26, and column 0 and column 1 arecolumns of built-in puncture bits. In a matrix block including row 5 torow 45 and column 2 to column 26, row 5 and row 6 are mutuallyorthogonal, row 29 and row 30 are mutually orthogonal, and so on. It maybe understood that if the base graph or the base matrix includes thesubmatrix D, when columns in the core matrix are switched with eachother, corresponding columns in the submatrix D also need to be switchedwith each other.

For example, if column 23 and column 25 in the core matrix are switchedwith each other, column 23 and column 25 in the submatrix D also need tobe switched with each other correspondingly.

Only examples are provided herein, and the examples do not constitute alimitation.

In the embodiments of the present application, the submatrix D has aquasi-orthogonal structure, and to be specific, two adjacent rows ineach column other than columns of built-in puncture bits are orthogonal.For example, in submatrices D provided in the base graph 30 a, the basegraph 80 a, a base graph 170 a as shown in FIG. 11 a , and the basegraph as shown in FIG. 12 according to the embodiments of the presentapplication, column 0 and column 1 are columns of built-in puncturebits, and two adjacent rows in each of other columns are orthogonal. Itshould be noted that the columns of built-in puncture bits may be othercolumns. This is not limited herein.

In another possible implementation, the matrix F with thequasi-orthogonal structure may also include at least two orthogonalrows, and there is a maximum of only one non-zero-element in each ofcolumn 0 to column 26 in two adjacent rows among the at least twoorthogonal rows. For example, if m_(D)>30, a corresponding code ratesupported by the LDPC code is less than 2/5, and a submatrix includingthe last 11 rows in the matrix F, that is, row 30 to row 40 in thematrix F, and column 0 to column 26 may be orthogonal. To be specific,in the matrix F, there is a maximum of only one non-zero-element in acolumn other than columns of built-in puncture bits in two adjacent rowsamong row 0 to row 29, and there is a maximum of only onenon-zero-element in each of column 0 to column 26 in two adjacent rowsamong the row 30 to row 40.

For another example, a submatrix including row 26 to row 40 and column 0to column 26 in the matrix F may be orthogonal. To be specific, in thematrix F, there is a maximum of only one non-zero-element in a columnother than columns of built-in puncture bits in two adjacent rows amongrow 0 to row 25, and there is a maximum of only one non-zero-element ineach of column 0 to column 26 in two adjacent rows among row 26 to row40. In the base graph 170 a shown in FIG. 11 a , the matrix F is amatrix including row 5 to row 45 and column 0 to column 26 in the basegraph, the matrix F has a quasi-orthogonal structure, row 26 to row 40in the matrix F are orthogonal, and there is a maximum of only onenon-zero-element in each column in two adjacent rows among row 26 to row40.

A core matrix in the base graph 170 a is the same as the core matrix inthe base graph 80 a. For the submatrix D at each code rate, changes maybe made to one or two non-zero-elements or one or two zero-elements ineach row without affecting performance of the submatrix D.

For another example, if m_(D)>20, a submatrix including the last 21 rowsin the matrix F, that is, row 25 to row 45 in the matrix F, and column 0to column 26 may be orthogonal. To be specific, in the matrix F, thereis a maximum of only one non-zero-element in a column other than columnsof built-in puncture bits in two adjacent rows among row 0 to row 19,and there is a maximum of only one non-zero-element in each of column 0to column 26 in two adjacent rows among row 20 to row 40. A core matrixin the base graph 170 a shown in FIG. 11 a is the same as the corematrix in the base graph 80 a. Row 5 to row 45 meet a quasi-orthogonalstructure, or row 5 to row 25 meet a quasi-orthogonal structure, and row25 to row 45 meet a quasi-orthogonal structure.

A core matrix in a base graph shown in FIG. 12 is the same as the corematrix in the base graph 80 a, and row 5 to row 45 in the core matrixhas a quasi-orthogonal structure.

A base matrix 30 c shown in FIG. 3 c -1 is a base matrix example of thebase graph 30 a shown in FIG. 3 a . A non-zero-element in row i andcolumn j in the base graph 30 a has a same position in the base matrix30 c, and a value of the non-zero-element is a shift value P_(i,j). Thesubmatrix D includes m_(D) rows in a shift matrix of the matrix F. Forthe base matrix 30 c shown in FIG. 3 c -1, m_(D)=41, and m_(D) may beselected based on different code rates. A shift matrix corresponding tothe submatrix D is the shift matrix of the matrix F. Herein the shiftmatrix of the matrix F is obtained by replacing a non-zero-element inrow i and column j in the matrix F with a shift value P_(i,j), and azero-element is represented by −1 or null in the shift matrix. It shouldbe noted that only examples are provided herein, the base graph may be80 a, 180 a, or the like, and base graphs are not described one by oneherein.

In a possible implementation, the shift matrix of the matrix F mayinclude rows or columns in any one of matrices 30 c-1 to 30 c-10 shownin FIG. 3 c -2 to FIG. 3 c -11. For example,

if a lifting factor Z is one of {16, 18, 20, 22, 24, 26, 28, 30}, theshift matrix of the matrix F may be the matrix 30 c-1 shown in FIG. 3 c-2 or a matrix obtained by performing row/column permutation on thematrix 30 c-1; or

if a lifting factor Z is one of {32, 36, 40, 44, 48, 52, 56, 60}, theshift matrix of the matrix F may be the matrix 30 c-2 shown in FIG. 3 c-3 or a matrix obtained by performing row/column permutation on thematrix 30 c-2; or

if a lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112, 120},the shift matrix of the matrix F may be the matrix 30 c-3 shown in FIG.3 c -4 or a matrix obtained by performing row/column permutation on thematrix 30 c-3; or

if a lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be the matrix 30 c-4 shown inFIG. 3 c -5 or a matrix obtained by performing row/column permutation onthe matrix 30 c-4; or

if a lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be the matrix 30 c-5 shown in FIG. 3 c -6 ora matrix obtained by performing row/column permutation on the matrix 30c-5.

A submatrix D in the base matrix 30 c is replaced by m_(D) rows in eachshift matrix of the matrix F, to obtain base matrices that are ofdifferent code rates and correspond to the base graph 30 a. If m_(D)=41,a matrix including row 5 to row 45 and column 0 to column 26 in the basematrix 30 c is replaced by each shift matrix of the matrix F, to obtaineach base matrix of 46 rows and 68 columns that corresponds to the basegraph 30 a. In this case, a code rate is 1/3.

In another possible implementation, a lifting factor set may be {24, 26,28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112,120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384},and one of the following may be selected:

if a lifting factor Z is one of {24, 26, 28, 30}, the shift matrix ofthe matrix F may be the matrix 30 c-6 shown in FIG. 3 c -7 or a matrixobtained by performing row/column permutation on the matrix 30 c-6; or

if a lifting factor Z is one of {32, 36, 40, 44}, the shift matrix ofthe matrix F may be the matrix 30 c-7 shown in FIG. 3 c -8 or a matrixobtained by performing row/column permutation on the matrix 30 c-7; or

if a lifting factor Z is one of {48, 52, 56, 60}, the shift matrix ofthe matrix F may be the matrix 30 c-8 shown in FIG. 3 c -9 or a matrixobtained by performing row/column permutation on the matrix 30 c-8; or

if a lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112, 120},the shift matrix of the matrix F may be the matrix 30 c-3 shown in FIG.3 c -4 or a matrix obtained by performing row/column permutation on thematrix 30 c-3; or

if a lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be the matrix 30 c-4 shown inFIG. 3 c -5 or a matrix obtained by performing row/column permutation onthe matrix 30 c-4; or

if a lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be the matrix 30 c-5 shown in FIG. 3 c -6 ora matrix obtained by performing row/column permutation on the matrix 30c-5.

Based on the foregoing implementations, in another possibleimplementation, there are more choices for the shift matrix of thematrix F to further improve performance. For example, the shift matrixof the matrix F may be the matrix 30 c-9 shown in FIG. 3 c -10 or amatrix obtained by performing row/column permutation on the matrix 30c-9, or the matrix 30 c-10 shown in FIG. 3 c -11 or a matrix obtained byperforming row/column permutation on the matrix 30 c-10. For example, alifting factor may be designed as follows:

if the lifting factor Z is one of {24, 26, 28, 30}, the shift matrix ofthe matrix F may be the matrix 30 c-6 shown in FIG. 3 c -7 or a matrixobtained by performing row/column permutation on the matrix 30 c-6; or

if the lifting factor Z is one of {32, 36, 40, 44}, the shift matrix ofthe matrix F may be the matrix 30 c-7 shown in FIG. 3 c -8 or a matrixobtained by performing row/column permutation on the matrix; or

if the lifting factor Z is one of {48, 52, 56, 60}, the shift matrix ofthe matrix F may be the matrix 30 c-8 shown in FIG. 3 c -9 or a matrixobtained by performing row/column permutation on the matrix 30 c-8; or

if the lifting factor Z is one of {64, 72, 80, 88}, the shift matrix ofthe matrix F may be the matrix 30 c-9 shown in FIG. 3 c -10 or a matrixobtained by performing row/column permutation on the matrix 30 c-9, orthe matrix 30 c-10 shown in FIG. 3 c -11 or a matrix obtained byperforming row/column permutation on the matrix 30 c-10; or

if the lifting factor Z is one of {96, 104, 112, 120}, the shift matrixof the matrix F may be the matrix 30 c-3 shown in FIG. 3 c -4 or amatrix obtained by performing row/column permutation on the matrix 30c-3; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be the matrix 30 c-4 shown inFIG. 3 c -5 or a matrix obtained by performing row/column permutation onthe matrix 30 c-4; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be the matrix 30 c-5 shown in FIG. 3 c -6 ora matrix obtained by performing row/column permutation on the matrix 30c-5.

In another possible implementation, the shift matrix of the matrix F mayinclude rows or columns in any one of matrices 80 c-1 to 80 c-9 shown inFIG. 8 c -2 to FIG. 8 c -10. For example, a lifting factor set may be{24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96,104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320,352, 384}, and one of the following may be selected:

if a lifting factor Z is one of {24, 26, 28, 30}, the shift matrix ofthe matrix F may be the matrix 80 c-1 shown in FIG. 8 c -2 or a matrixobtained by performing row/column permutation on the matrix 80 c-1; or

if a lifting factor Z is one of {32, 36, 40, 44}, the shift matrix ofthe matrix F may be the matrix 80 c-2 shown in FIG. 8 c -3 or a matrixobtained by performing row/column permutation on the matrix 80 c-2; or

if a lifting factor Z is one of {48, 52, 56, 60}, the shift matrix ofthe matrix F may be the matrix 80 c-3 shown in FIG. 8 c -4 or a matrixobtained by performing row/column permutation on the matrix 80 c-3; or

if a lifting factor Z is one of {60, 64, 72, 80, 88, 96, 104, 112, 120},the shift matrix of the matrix F may be the matrix 80 c-4 shown in FIG.8 c -5 or a matrix obtained by performing row/column permutation on thematrix 80 c-4; or

if a lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be the matrix 80 c-5 shown inFIG. 8 c -6 or a matrix obtained by performing row/column permutation onthe matrix 80 c-5; or

if a lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be the matrix 80 c-6 shown in FIG. 8 c -7 ora matrix obtained by performing row/column permutation on the matrix 80c-6.

Based on the foregoing implementations, in another possibleimplementation, to further improve performance, lifting factors Z may bedesigned at a finer granularity, so that there are more choices for theshift matrix of the matrix F. For example, the shift matrix of thematrix F may be the matrix 80 c-7 or a matrix obtained by performingrow/column permutation on the matrix, or the matrix 80 c-8 or a matrixobtained by performing row/column permutation on the matrix. Forexample, a lifting factor may be designed as follows:

if the lifting factor Z is one of {24, 26, 28, 30}, the shift matrix ofthe matrix F may be the matrix 80 c-1 shown in FIG. 8 c -2 or a matrixobtained by performing row/column permutation on the matrix 80 c-1; or

if the lifting factor Z is one of {32, 36, 40, 44}, the shift matrix ofthe matrix F may be the matrix 80 c-2 shown in FIG. 8 c -3 or a matrixobtained by performing row/column permutation on the matrix 80 c-2; or

if the lifting factor Z is one of {48, 52, 56, 60}, the shift matrix ofthe matrix F may be the matrix 80 c-3 shown in FIG. 8 c -4 or a matrixobtained by performing row/column permutation on the matrix 80 c-3; or

if the lifting factor Z is one of {64, 72, 80, 88}, the shift matrix ofthe matrix F may be the matrix 80 c-7 shown in FIG. 8 c -8 or a matrixobtained by performing row/column permutation on the matrix 80 c-7, orthe matrix 80 c-8 shown in FIG. 8 c -9 or a matrix obtained byperforming row/column permutation on the matrix 80 c-8; or

if the lifting factor Z is one of {96, 104, 112, 120}, the shift matrixof the matrix F may be the matrix 80 c-4 shown in FIG. 8 c -5 or amatrix obtained by performing row/column permutation on the matrix 80c-4; or

if the lifting factor Z is one of {128, 144, 160, 176, 192, 208, 224,240}, the shift matrix of the matrix F may be the matrix 80 c-5 shown inFIG. 8 c -6 or a matrix obtained by performing row/column permutation onthe matrix 80 c-5; or

if the lifting factor Z is one of {256, 288, 320, 352, 384}, the shiftmatrix of the matrix F may be the matrix 80 c-6 shown in FIG. 8 c -7 ora matrix obtained by performing row/column permutation on the matrix 80c-6.

In another possible implementation, if the lifting factor Z is any oneof {15, 30, 60, 120, 240}, the shift matrix of the matrix F may be thematrix 80 c-9 shown in FIG. 8 c -10 or a matrix obtained by performingrow/column permutation on the matrix 80 c-9. Further, when Z is greaterthan or equal to 24, performance of the shift matrix of the matrix F isrelatively high when the shift matrix is 80 c-9.

Likewise, rows may be switched with each other, and columns may also beswitched with each other in a base matrix. If at least one of rowpermutation or column permutation is performed on a base graph, samepermutation is also performed on a corresponding base matrix.

It can be learned that, in the foregoing implementations, 80 c-1 is abase matrix obtained by performing row permutation on base matrix 30c-6. 80 c-2 is a base matrix obtained by performing row permutation onbase matrix 30 c-7. 80 c-3 is a base matrix obtained by performing rowpermutation on base matrix 30 c-8. 80 c-4 is a base matrix obtained byperforming row permutation on base matrix 30 c-3. 80 c-5 is a basematrix obtained by performing row permutation on base matrix 30 c-4. 80c-6 is a base matrix obtained by performing row permutation on basematrix 30 c-5. 80 c-7 is a base matrix obtained by performing rowpermutation on base matrix 30 c-9. 80 c-8 is a base matrix obtained byperforming row permutation on base matrix 30 c-10.

A submatrix D in a base matrix 80 c is replaced by m_(D) rows in eachshift matrix of the matrix F, to obtain base matrices that are ofdifferent code rates and correspond to the base graph 80 a. If m_(D)=41,a matrix including row 5 to row 45 and column 0 to column 26 in the basematrix 80 c is replaced by each shift matrix of the matrix F, to obtaineach base matrix of 46 rows and 68 columns that corresponds to the basegraph 80 a. In this case, a code rate is 1/3.

It should be noted that because rows may be switched with each other andcolumns may be switched with each other in a base graph and a basematrix, in a possible implementation, the core matrix in the base graph30 a may be used as a core matrix in the base graph, that is, a partincluding a submatrix A and a submatrix B, and a submatrix D in the basegraph may include m_(D) rows in a matrix including row 5 to row 45 andcolumn 0 to column 26 in the base graph 30 a. Correspondingly, a corematrix in the base matrix may be one of 30 b-3, 30 b-4, 30 b-5, 30 b-6,30 b-7, 30 b-8, 30 b-9, or 30 b-10, and a corresponding submatrix D mayinclude m_(D) rows in any one of the following matrices: 30 c-3, 30 c-4,30 c-5, 30 c-6, 30 c-7, 30 c-8, 30 c-9, or 30 c-10. The core matrix andthe corresponding submatrix D may be selected based on a lifting factor.

In another possible implementation, the core matrix in the base graph 80a may be used as a core matrix in a base graph, that is, a partincluding a submatrix A and a submatrix B, and a submatrix D in the basegraph may include m_(D) rows in a matrix including row 5 to row 45 andcolumn 0 to column 26 in the base graph 80 a. Correspondingly, a corematrix in a base matrix may be one of 80 b-1, 80 b-2, 80 b-3, 80 b-4, 80b-5, 80 b-6, 80-7, 80 b-8, or 80 b-9, and a corresponding submatrix Dmay include m_(D) rows in any one of the following matrices: 80 c-1, 80c-2, 80 c-3, 80 c-4, 80 c-5, 80 c-6, 80 c-7, 80 c-8, or 80 c-9. The corematrix and the corresponding submatrix D may be selected based on alifting factor.

In another possible implementation, the core matrix in the base graph 80a may be used as a core matrix in a base graph, that is, a partincluding a submatrix A and a submatrix B, and a submatrix D in the basegraph may include m_(D) rows in a matrix including row 5 to row 45 andcolumn 0 to column 26 in the base graph 170 a, as shown in the basegraph 170 a. Correspondingly, a base matrix may include m_(D) rows inrow 5 to row 45 and row 0 to row 4 in a base matrix 170 b shown in FIG.11 b.

In another possible implementation, the core matrix in the base graph 80a may be used as a core matrix in a base graph, and a submatrix D in thebase graph may include m_(D) rows in a matrix including row 5 to row 45and column 0 to column 26 in the base graph shown in FIG. 12 .

It may be understood that in this application, the quasi-orthogonalstructure is not limited only to two adjacent rows, a matrix that meetsthe quasi-orthogonal structure may be designed to include a plurality ofgroups, each group includes at least two rows, for example, three rowsor four rows, and rows included in each group are quasi-orthogonal.

In performance curve diagrams shown in FIG. 4 and FIG. 5 , LDPC 1indicates that the LDPC code is obtained by encoding based on basematrices corresponding to the base graph 30 a, and LDPC 2 indicates acommon LDPC code for comparison. A horizontal coordinate indicates alength of an information bit sequence, and a unit of the length is bit.A vertical coordinate is a symbol signal-to-noise ratio (Es/N0).Performance curves indicate performance of a symbol signal-to-noiseratio for LDPC 1 and LDPC 2 in cases of different information bitsequence lengths when BLERs are respectively 0.01 and 0.0001. A coderate R is 8/9 in FIG. 4 , and a code rate R is 1/3 in FIG. 5 . It can belearned that at a same BLER, a symbol signal-to-noise ratio of LDPC 1 isless than that of LDPC 2 in cases of different information bit sequencelengths, that is, performance of LDPC 1 is better than that of LDPC 2.

In an encoding method provided in an embodiment of the presentapplication, an encoder encodes an input sequence by using an LDPCmatrix. A base graph of the LDPC matrix may be any base graph in theforegoing examples, and a base matrix H_(B) of the LDPC matrix may beany base matrix in the foregoing examples. The input sequence of theencoder may be an information bit sequence, or may be an information bitsequence obtained after at least one of the following processing: CRCattachment or filler bits insertion.

The encoding method further includes: determining a lifting factor Z. Avalue of the lifting factor Z may be determined based on a length K ofthe input sequence. Sometimes the information bit sequence is alsoreferred to as a code block, and may be obtained by performing codeblock division on a transport block. If a length of the information bitsequence is Kc, a minimum value that meets 22*Z≥Kc may be determinedfrom a plurality of lifting factors defined in the system. For example,if Kc=3800, and the lifting factors defined in the system include 16,18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80,88, 96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288,320, 352, and 384, it may be determined that Z is 176. It should benoted that only examples are provided herein, and the examples do notconstitute a limitation.

In a possible design, filling may be performed on the information bitsequence to obtain the input sequence, so that the length of the inputsequence is K=K_(b)*Z, that is, Z=K/K_(b). For example, values of fillerbits may be null, 0, or other values agreed in the system. After theencoding, these filler bits can be identified and are not sent, whichdoes not constitute a limitation in the present application.

That the encoder encoding the input sequence by using the LDPC matrix Hmay be encoding the input sequence by using the LDPC matrixcorresponding to the lifting factor Z.

In a possible implementation, the input sequence is c={c₀, c₁, c₂, . . ., c_(K−1)}, a length of the input sequence c is K, and an outputsequence obtained after the encoder encodes the input sequence c isd={d₀, d₁, d₂, . . . , d_(N−1)}. K is an integer greater than 0, and Kmay be an integer multiple of the lifting factor Z.

The output sequence d includes K₀ bits in the input sequence c andparity bits in a parity sequence w, K₀ is an integer greater than 0 andless than or equal to K, a length of the parity sequence w is N−K₀, andw={w₀, w₁, w₂, . . . , w_(N−K) _(o) ⁻¹}.

The parity sequence w and the input sequence c meet Formula (1):

$\begin{matrix}{{H \times \begin{bmatrix}c^{T} \\w^{T}\end{bmatrix}} = 0^{T}} & (1)\end{matrix}$

where c^(T)=[c₀, c₁, c₂, . . . , c_(K−1)]^(T), c^(T) is a transposedvector of a vector including bits in the input sequence, w^(T)=[w₀, w₁,w₂, . . . , w_(N−K) ₀ ⁻¹]^(T), w^(T) is a transposed vector of a vectorincluding bits in the parity sequence, 0^(T) is a column vector, andvalues of all elements of 0^(T) are 0.

H is an LDPC matrix obtained according to any base graph described inthe foregoing embodiments, and a base graph of H has m rows and ncolumns, and may be any base graph described in the foregoingembodiments, for example, 30 a, 80 a, 170 a, and the base graph shown inFIG. 12 .

In a design, the base graph of H includes p columns of built-in puncturebits, p is an integer greater than or equal to 0, information bitscorresponding to the p columns of built-in puncture bits are not output,and the output sequence does not include the information bitscorresponding to the p columns of built-in puncture bits. In this case,K₀=K−p×Z. For example, if p=2, K₀=K−2×Z, and the length of the paritysequence w is N+2×Z−K. If the p columns of built-in puncture bitsparticipate in encoding, K₀=K, and the length of the parity sequence wis N−K.

Correspondingly, H may have M rows and (N+p×Z) columns or M rows and Ncolumns, the base graph of H has M/Z rows and (N+p×Z)/Z columns.

The base graph of the LDPC matrix H may be represented by [H_(BG)H_(BG,EXT)],

${H_{{BG},{EXT}} = \begin{bmatrix}0_{m_{c} \times n_{c}} \\I_{n_{c} \times n_{c}}\end{bmatrix}},0_{m_{c} \times n_{c}}$represents an all-zero matrix of size m_(c)×n_(c), and I_(n) _(c) _(×n)_(c) represents an identity matrix of size n_(c)×n_(c).

In a possible design, if 0_(m) _(c) _(×n) _(c) is the submatrix C in thebase graph in the foregoing embodiments, and I_(n) _(c) _(×n) _(c) isthe submatrix E in the foregoing embodiments,

$H_{BG} = \begin{bmatrix}\begin{bmatrix}A & B\end{bmatrix} \\D\end{bmatrix}$where A, B, and D are respectively the submatrix A, the submatrix B, andthe submatrix D in the base graph in the foregoing embodiments, m_(c)=5,0≤n_(c)≤41, a row count of H_(BG) is less than or equal to 46 andgreater than or equal to 5, and a column count of H_(BG) is equal to 27.

In another possible design, because column 26 is a weight-1 matrixcolumn, and a non-zero-element in column 26 is located in row 5, 0_(m)_(c) _(×n) _(c) may also include the first four rows in column 26 in thebase graph in the foregoing embodiments and the first four rows in thesubmatrix C in the foregoing embodiments. I_(n) _(c) _(×n) _(c) may alsoinclude the submatrix E in the base graph in the foregoing embodiments,row 5 to row 46 in column 26, and a last row in the submatrix C, wherem_(c)4, 0≤n_(c)≤42. H_(BG) is a matrix obtained after a last column isremoved from a part including the submatrix A, the submatrix B, and thesubmatrix D in the base graph in the foregoing embodiments. A row countof H_(BG) is less than or equal to 46 and greater than or equal to 5,and a column count of H_(BG) is equal to 26. Optionally, if a code rateneeds to be further increased, H_(BG) may have four rows: row 0 to row3.

Correspondingly, the LDPC matrix H may be represented by H=[H₁H₂].

H₁ may be obtained after each zero-element in H_(BG) is replaced by aZ*Z all-zero matrix and each non-zero-element is replaced by a Z*Zcircular permutation matrix h_(i,j). The circular permutation matrixh_(i,j) is obtained by circularly shifting the identity matrix of sizeZ*Z to the right P_(i,j) times, and sometimes is represented byI(P_(i,j)), where i is a row index, and j is a column index. In apossible design, P_(i,j)=mod(V_(i,j), Z), and V_(i,j) of anon-zero-element in row i and column j in a base matrix corresponds to alifting factor set index corresponding to Z.

H₂ may be obtained after each zero-element in H_(BG,EXT) is replaced bya Z*Z all-zero matrix and each non-zero-element is replaced by a Z*Zidentity matrix.

The encoder may perform encoding and outputting in a plurality ofmanners. Any one of the base graph shown in FIG. 12 , the base graph 80a, or the base graph 170 a described in the foregoing embodiment is usedas an example for description below. The base graph has a maximum of 46rows and a maximum of 68 columns and includes two columns of built-inpuncture bits. For ease of description, a base graph that has the mostrows and the most columns is sometimes referred to as a complete basegraph in the present application.

Manner 1:

Encoding is performed based on the complete base graph, so that as manyparity bits as possible can be obtained. In this case, m=46, and n=68,which correspond to row 0 to row 45 and column 0 to column 67 in any oneof the foregoing base graphs.

Correspondingly, M=46*Z for the LDPC matrix H. If the output sequenceincludes the information bits corresponding to the columns of built-inpuncture bits, N=68*Z; or if the output sequence does not include the2*Z information bits corresponding to the columns of built-in puncturebits, N=66*Z.

During subsequent processing, one or more information bits and one ormore parity bits that need to be sent may be determined from the outputsequence generated by the encoder.

Manner 2:

Encoding is performed based on some rows and some columns in thecomplete base graph. A row and a column may be selected, based on a coderate that needs to be sent, or a quantity of information bits and aquantity of parity bits, or the like, from the complete base graph forencoding.

For example, the code rate is 8/9, m=5, and n=27, that is, encoding isperformed based on row 0 to row 4 and column 0 to column 26 in any oneof the foregoing base graphs.

Correspondingly, M=5*Z for the LDPC matrix H. If the output sequenceincludes the information bits corresponding to the columns of built-inpuncture bits, N=27*Z; or if the output sequence does not include theinformation bits corresponding to the columns of built-in puncture bits,N=25*Z.

For another example, the code rate is 1/3, m=46, and n=68.

It can be learned that in this manner, size of the base graph of H meet5≤m≤46 and 27≤n≤68, and correspondingly, for the LDPC matrix H,5×Z≤M≤46×Z and 27×Z≤N≤68×Z.

In a possible design, the 26^(th) column in any base graph describedabove is a weight-1 matrix column, and puncturing may be performed onthe weight-1 matrix column in the core matrix, so that the core matrixis decreased by one row and one column accordingly, and m=4 and n=26,that is, encoding is performed based on row 0 to row 3 and column 0 tocolumn 25 in any base graph described above. A higher code rate can beobtained in this manner. Therefore, size of the base graph meet 4≤m≤46and 26≤n≤68, and correspondingly, for the LDPC matrix H, 4×Z≤M≤46×Z and26×Z≤N≤68×Z.

In the foregoing implementations, the base matrix H_(B) of the LDPCmatrix H may be any base matrix described in the foregoing embodimentsor a base matrix obtained by performing row permutation, or columnpermutation, or row permutation and column permutation on any basematrix described above. A base graph of the base matrix H_(B) includesat least a submatrix A and a submatrix B, and may further include asubmatrix C, a submatrix D, and a submatrix E. For the submatrices,refer to the descriptions in the foregoing embodiments, and details arenot described herein again. Certainly, the base matrix H_(B) may beanother base matrix whose base graph complies with the base graph shownin the foregoing embodiments, and the base matrix H_(B) is not limitedthereto in the present application.

In a possible implementation, a base matrix H_(B) of an LDPC code may bestored in a memory, and the encoder obtains an LDPC matrix correspondingto a lifting factor Z, so as to encode the input sequence.

In another possible implementation, because there are a plurality ofbase matrices H_(B) of an LDPC code, and relatively large storage spaceis occupied if the base matrices H_(B) are stored based on a matrixstructure, a base graph of the LDPC code may be stored in a memory,shift values of non-zero-elements in each base matrix may be stored byrow or by column, and then an LDPC matrix may be obtained based on thebase graph and a shift value in a base matrix corresponding to a liftingfactor Z.

The base graph may indicate a position of the non-zero-element in eachbase matrix. In another possible implementation, storing a base graphmay be storing a position of a non-zero-element in the base graph. Theposition of the non-zero-element may be indicated by a row and a columnin which the non-zero-element is located, for example, a position of acolumn in which a non-zero-element in each row is located, or a positionof a row in which a non-zero-element in each column is located. Inanother possible implementation, storing a base graph may be storing aposition of a zero-element in the base graph. Likewise, the position ofthe zero-element may also be indicated by a row and a column in whichthe zero-element is located, for example, a position of a column inwhich a zero-element in each row is located, or a position of a row inwhich a zero-element in each column is located, and a correspondingposition of a non-zero-element may be obtained by excluding the positionof the zero-element. It should be noted that only examples are providedherein, and the examples do not constitute a limitation in the presentapplication.

In a design, parameters related to a base graph or a base matrix may beexpressed in a table. For example, related parameters or tables may bestored in one or more memories. Related parameters such as a row indexof a base graph or a base matrix, or a column in which anon-zero-element is located are read from the memory, so as to obtainthe base graph or the base matrix. Optionally, a weight of each row anda shift value of a non-zero-element in each row may be further stored.

Base graph 170 a in FIG. 11 a is used as an example for descriptionbelow. For another base graph or base matrix provided in thisapplication, refer to similar designs.

For example, the core matrix in the base graph 80 a, the base graph 170a, or the base graph shown in FIG. 12 may be expressed in Table 3.

TABLE 3 Column index of non-zero-elements Row index Row weight in row 019 0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23 119 0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24 219 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25 319 0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25 43 0, 1, 26

For example, a base graph of an LDPC matrix may include a core partshown in Table 3. Another part of the base graph of the LDPC matrix maybe shown in the base graph 80 a, the base graph 170 a, or the base graphshown in FIG. 12 , or another structure described in this application,or another matrix structure, and this is not limited in thisapplication.

The base graph 170 a is used as another example. Parameters related tothe first 24 rows in the base graph may be shown in Table 4. Parametersrelated to other rows are similar and are not listed in Table 4 due tospace limitation.

TABLE 4 Column index of non-zero-elements Row index Row weight in row 019 0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23 119 0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24 219 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25 319 0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25 43 0, 1, 26 5 8 0, 1, 3, 12, 16, 21, 22, 27 6 9 0, 6, 10, 11, 13, 17, 18,20, 28 7 7 0, 1, 4, 7, 8, 14, 29 8 10 0, 1, 3, 12, 16, 19, 21, 22, 24,30 9 9 0, 1, 10, 11, 13, 17, 18, 20, 31 10 7 1, 2, 4, 7, 8, 14, 32 11 80, 1, 12, 16, 21, 22, 23, 33 12 7 0, 1, 10, 11, 13, 18, 34 13 6 0, 3, 7,20, 23, 35 14 7 0, 12, 15, 16, 17, 21, 36 15 7 0, 1, 10, 13, 18, 25, 3716 6 1, 3, 11, 20, 22, 38 17 6 0, 14, 16, 17, 21, 39 18 6 1, 12, 13, 18,19, 40 19 6 0, 1, 7, 8, 10, 41 20 6 0, 3, 9, 11, 22, 42 21 6 1, 5, 16,20, 21, 43 22 5 0, 12, 13, 17, 44 23 5 1, 2, 10, 18, 45 . . . . . . . ..

It should be noted that only examples are provided herein, and theexamples do not constitute a limitation. Related parameters of anotherbase graph or base matrix provided in this application may also beexpressed in a similar table. It may be understood that the base graph170 a, Table 3, and Table 4 are intended to help understand design ofthe base graph and the base matrix. A representation form is not limitedonly to the base graph 170 a or a representation form in Table 3 orTable 4. Another possible variation may be included.

In an implementation, a column index, a column weight, and a row inwhich a non-zero-element is located or a row in which a zero-element islocated, for example, a form in Table 5 may be used.

TABLE 5 Row index of non-zero-elements Column index Column weight incolumn 0 5 0, 1, 2, 3, 4 1 4 0, 2, 3, 4, 2 3 0, 1, 2 3 3 0, 1, 3 4 3 1,2, 3 5 3 0, 1, 2 6 3 0, 2, 3 7 3 1, 2, 3 8 3 1, 2, 3 9 3 0, 1, 2 10 3 0,2, 3 11 3 0, 1, 3 12 3 0, 1, 3 13 3 0, 2, 3 14 3 1, 2, 3 15 3 0, 1, 2 163 0, 1, 3 17 3 1, 2, 3 18 3 0, 2, 3 19 3 0, 1, 2 20 3 0, 2, 3 21 3 0, 1,3 22 3 0, 1, 3 23 2 0, 1 24 2 1, 2 25 2 2, 3 26 1 4

In an implementation, the parameter “row weight” or “column weight” inTable 3, Table 4, or Table 5 may be omitted. A quantity ofnon-zero-elements in a row or a column may be learned from a column or arow in which a non-zero-element is located in the row or the column.Therefore, a row weight or a column weight is also learned.

In an implementation, parameter values in “column in which anon-zero-element is located” in Table 3 or Table 4 or parameter valuesin “row in which a non-zero-element is located” in Table 5 may not besorted in ascending order provided that a column in which anon-zero-element is located or a row in which a non-zero-element islocated can be retrieved in the parameter values.

In an implementation, Table 3 or Table 4 may further include a column of“shift value of a non-zero-element”, and parameter values in the columnof “shift value of a non-zero-element” are in a one-to-onecorrespondence with parameter values in “column in which anon-zero-element is located”. Table 5 may further include a column of“shift value of a non-zero-element”, and parameter values in the columnof “shift value of a non-zero-element” are in a one-to-onecorrespondence with parameter values in “row in which a non-zero-elementis located”.

In a design, to save storage space, a position of a non-zero-element ina part with a relatively fixed structure in a base graph may becalculated based on a row index or a column index without the positionbeing stored. For example, a submatrix E is a diagonal matrix, andincludes a non-zero-element only on a diagonal. A position of a columnin which a non-zero-element is located in the submatrix E may becalculated based on a row index, or a position of a row in which anon-zero-element is located may be calculated based on a column index.In an example of any one of the base graph 80 a, the base graph 170 a,or the base graph in FIG. 12 , an index of a column in which anon-zero-element in row m_(e) is located is m_(e)+K_(b), where m_(e)≥4,and K_(b)=22. For example, a column in which a non-zero-element in row 7is located is column 29. For another example, a i-diagonal structure B′in a submatrix B is located in row 0 to row 3 and column 23 to column 25in any one of the base graph 80 a, the base graph 170 a, or the basegraph shown in FIG. 12 . A column index of a column in which anon-zero-element in the bi-diagonal structure B′ is located may becalculated based on a row index, or a row index of a row in which anon-zero-element is located may be calculated based on a column index.Positions of non-zero-elements in row m_(B) include column m_(B)+K_(b)and column m_(B)+K_(b)+1, where 0<m_(B)<3. A position of anon-zero-element in row m_(B) is column m_(B)+K_(b), where m_(B)=0 orm_(B)=3. For another example, for a weight-1 matrix column in asubmatrix B, that is, column 26 in any one of the base graph 80 a, thebase graph 170 a, or the base graph in FIG. 12 , a position of anon-zero-element in row m_(B) is column m_(B)+K_(b), where m_(B)=4.

Table 6 shows parameters related to the rows in FIG. 12 . Positions ofcolumns in which non-zero-elements in column 0 to column 25 are locatedmay be stored whereas positions of columns in which non-zero-elements incolumn 26 to column 68 are located are not stored, that is, columns inwhich non-zero-elements in weight-1 matrix columns in the submatrix Eand the submatrix B are located are not stored. Table 6 may be used torepresent H_(BG) whose column index is 26.

TABLE 6 Column index in which a non-zero-element Row index Row weight islocated 0 19 0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20,21, 22, 23 1 19 0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21,22, 23, 24 2 19 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19,20, 24, 25 3 19 0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20,21, 22, 25 4 2 0, 1 5 7 0, 1, 3, 12, 16, 21, 22 6 8 0, 6, 10, 11, 13,17, 18, 20 7 6 0, 1, 4, 7, 8, 14 8 9 0, 1, 3, 12, 16, 19, 21, 22, 24 9 80, 1, 10, 11, 13, 17, 18, 20 10 6 1, 2, 4, 7, 8, 14 11 7 0, 1, 12, 16,21, 22, 23 12 6 0, 1, 10, 11, 13, 18 13 5 0, 3, 7, 20, 23 14 6 0, 12,15, 16, 17, 21 15 6 0, 1, 10, 13, 18, 25 16 5 1, 3, 11, 20, 22 17 5 0,14, 16, 17, 21 18 5 1, 12, 13, 18, 19 19 5 0, 1, 7, 8, 10 20 5 0, 3, 9,11, 22 21 5 1, 5, 16, 20, 21 22 4 0, 12, 13, 17 23 4 1, 2, 10, 18 24 50, 3, 4, 11, 22 25 4 1, 6, 7, 14 26 4 0, 2, 4, 15 27 3 1, 6, 8 28 4 0,4, 19, 21 29 4 1, 14, 18, 25 30 4 0, 10, 13, 24 31 4 1, 7, 22, 25 32 40, 12, 14, 24 33 4 1, 2, 11, 21 34 4 0, 7, 15, 17 35 4 1, 6, 12, 22 36 40, 14, 15, 18 37 3 1, 13, 23 38 4 0, 9, 10, 12 39 4 1, 3, 7, 19 40 3 0,8, 17 41 4 1, 3, 9, 18 42 3 0, 4, 24 43 4 1, 16, 18, 25 44 4 0, 7, 9, 2245 3 1, 6, 10

Table 7 shows parameters related to the rows in FIG. 12 . Positions ofcolumns in which non-zero-elements in column 0 to column 26 are locatedmay be stored whereas positions of columns in which non-zero-elements incolumn 27 to column 68 are located are not stored, that is, columns inwhich non-zero-elements in the submatrix E are located are not stored.Table 7 may be used to represent H_(BG) whose column index is 27.

TABLE 7 Column index in which a non-zero-element Row index Row weight islocated 0 19 0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20,21, 22, 23 1 19 0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21,22, 23, 24 2 19 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19,20, 24, 25 3 19 0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20,21, 22, 25 4 3 0, 1, 26 5 7 0, 1, 3, 12, 16, 21, 22 6 8 0, 6, 10, 11,13, 17, 18, 20 7 6 0, 1, 4, 7, 8, 14 8 9 0, 1, 3, 12, 16, 19, 21, 22, 249 8 0, 1, 10, 11, 13, 17, 18, 20 10 6 1, 2, 4, 7, 8, 14 11 7 0, 1, 12,16, 21, 22, 23 12 6 0, 1, 10, 11, 13, 18 13 5 0, 3, 7, 20, 23 14 6 0,12, 15, 16, 17, 21 15 6 0, 1, 10, 13, 18, 25 16 5 1, 3, 11, 20, 22 17 50, 14, 16, 17, 21 18 5 1, 12, 13, 18, 19 19 5 0, 1, 7, 8, 10 20 5 0, 3,9, 11, 22 21 5 1, 5, 16, 20, 21 22 4 0, 12, 13, 17 23 4 1, 2, 10, 18 245 0, 3, 4, 11, 22 25 4 1, 6, 7, 14 26 4 0, 2, 4, 15 27 3 1, 6, 8 28 4 0,4, 19, 21 29 4 1, 14, 18, 25 30 4 0, 10, 13, 24 31 4 1, 7, 22, 25 32 40, 12, 14, 24 33 4 1, 2, 11, 21 34 4 0, 7, 15, 17 35 4 1, 6, 12, 22 36 40, 14, 15, 18 37 3 1, 13, 23 38 4 0, 9, 10, 12 39 4 1, 3, 7, 19 40 3 0,8, 17 41 4 1, 3, 9, 18 42 3 0, 4, 24 43 4 1, 16, 18, 25 44 4 0, 7, 9, 2245 3 1, 6, 10

In the foregoing designs, the column of “row weight” is optional. In apossible design, 1 and 0 in each row or each column in a base graph maybe considered as binary numerals, and storing the binary numerals indecimal numerals or hexadecimal numerals can save storage space. Any oneof the foregoing base graphs is used as an example. Positions ofnon-zero-elements in the first 26 columns or the first 27 columns may bestored in four hexadecimal numerals in each row. For example, if thefirst 26 columns in row 0 are 11110110 01111101 10111111 00, positionsof non-zero-elements in row 0 may be denoted as 0xF6, 0x7D, 0xBF, and0x00. To be specific, every eight columns form one hexadecimal numeral.0 may be filled for the last two or three columns to obtain eightdigits, so that a corresponding hexadecimal numeral is obtained. Thesame is true of another row, and details are not described herein again.

When the information bit sequence is to be encoded, the base matrixH_(B) may be expanded based on the lifting factor Z to obtain the LDPCmatrix H used for encoding. A circular permutation matrix h_(i,j) ofsize Z*Z is determined for each P_(i,j) of non-zero-element in the basematrix H_(B), where h_(i,j) is a circular permutation matrix obtained bycircularly shifting an identity matrix P_(i,j) times. A non-zero-elementcorresponding to P_(i,j) is replaced by h_(i,j), and a zero-element inthe base matrix H_(B) is replaced by an all-zero matrix of size Z*Z, soas to obtain the parity-check matrix H.

In a possible design, for the lifting factor Z, P_(i,j) of an element inrow i and column j in the base matrix H_(B) may meet a relationshipshown in (2):

$\begin{matrix}{P_{i,j} = \left\{ \begin{matrix}{- 1} & {V_{i,j} = {- 1}} \\{{mod}\left( {V_{i,j},Z} \right)\ } & {V_{i,j} \geq 0}\end{matrix} \right.} & (2)\end{matrix}$

where V_(i,j) may be a shift value of an element in row i and column jin a base matrix of a set to which the lifting factor Z belongs, or ashift value of a non-zero-element in row i and column j in a base matrixcorresponding to a maximum lifting factor in a set to which the liftingfactor Z belongs.

A correspondence between a base matrix index and a set of liftingfactors Z that is shown in Table 2 is used as an example. Z=13, andP_(i,j) of an element in row i and column j in a base matrix of Z meets(2).

V_(i,j) is a shift value of a non-zero-element in row i and column j ina base matrix indicated by PCM 7. For Z=13, a modulo operation isperformed by taking the shift value V_(i,j) modulo Z, where Z=13, andV_(i,j) is a shift value of the non-zero-element in the row i and thecolumn j in the base matrix indicated by PCM 7.

It should be noted that only examples are provided herein, and theexamples do not constitute a limitation in the present application.

The base graph 80 a or the base graph 170 a is used as an example. Aftera base matrix H_(B) is determined, one or more parity bits correspondingto column 22 to column 25 in the base matrix may be first obtained byusing the input sequence and row 0 to row 3 and column 0 to column 25(i.e. H_(core-dual)). One or more parity bits corresponding to column 26(that is, a weight-1 matrix column) may be obtained based on the inputsequence and one or more parity bits corresponding to H_(core-dual). Theencoding may be performed based on the input sequence, the one or moreparity bits corresponding to column 22 to column 26, and a submatrix D,to obtain one or more parity bits corresponding to a submatrix E. Inthis way, encoding is completed. For an encoding process of an LDPCcode, refer to the descriptions in the foregoing implementations, anddetails are not described herein again.

In the communications system, the LDPC code may be obtained afterencoding is performed in the foregoing method. After the LDPC code isobtained, a communications apparatus may further perform one or more ofthe following operations: performing rate matching on the LDPC code;performing, based on an interleaving scheme, interleaving on an LDPCcode obtained after the rate matching; modulating, based on a modulationscheme, an LDPC code obtained after the interleaving, to obtain a bitsequence X; or sending the bit sequence X.

In a decoding method provided in another embodiment of the presentapplication, a decoder decodes an input sequence by using an LDPCmatrix. A base graph of the LDPC matrix may be any base graph in theforegoing examples, and a base matrix H_(B) of the LDPC matrix may beany base matrix in the foregoing examples. The input sequence of thedecoder may be a soft value sequence of an LDPC code.

The method further includes: determining a lifting factor Z. Acommunications device at a receive end may receive a signal including anLDPC code, obtain a soft value sequence of the LDPC code in the signal,and determine the corresponding lifting factor Z.

That the decoder decodes the input sequence by using the LDPC matrix Hmay be decoding the soft value sequence of the LDPC code by using anLDPC matrix H corresponding to the lifting factor Z.

Because decoding is an inverse process of encoding, for descriptions ofthe LDPC matrix H and the base graph of the LDPC matrix H, refer to theforegoing encoding embodiment. Decoding may be performed based on acomplete base graph, or decoding may be performed based on some rows orsome columns in a complete base graph.

The base matrix H_(B) of the LDPC matrix H may be any base matrixdescribed in the foregoing embodiments or a base matrix obtained byperforming row permutation, or column permutation, or row permutationand column permutation on any base matrix described above. A base graphof the base matrix H_(B) includes at least a submatrix A and a submatrixB, and may further include a submatrix C, a submatrix D, and a submatrixE. For the submatrices, refer to the descriptions in the foregoingembodiments, and details are not described herein again. Certainly, thebase matrix H_(B) may be another base matrix whose base graph complieswith the base graph shown in the foregoing embodiments, and the basematrix H_(B) is not limited thereto in the present application.

In a possible design, the base matrix H_(B) of the LDPC code may bestored in a memory, the soft value sequence of the LDPC code may bedecoded after the LDPC matrix corresponding to the lifting factor Z isobtained.

In another possible implementation, because there are a plurality ofbase matrices of an LDPC code, and relatively large storage space isoccupied if the base matrices are stored based on a matrix structure, abase graph of the LDPC code may be stored in a memory, shift values ofnon-zero-elements in each base matrix may be stored by row or by column,and then an LDPC matrix may be obtained based on the base graph and ashift value in a base matrix corresponding to a lifting factor Z.

The base graph may be stored in various manners described in theforegoing encoding embodiment.

It should be noted that only examples are provided herein, and theexamples do not constitute a limitation.

Decoding is an inverse process of encoding, and the base matrix H_(B)used during the decoding has a same characteristic as the base matrix inthe encoding method embodiment. For lifting the base matrix H_(B) toobtain the LDPC matrix H, also refer to the encoding method embodiment.

In the communications system, before the decoding method, acommunications apparatus may further perform one or more of thefollowing operations: receiving a signal including an LDPC code; orperforming demodulation, de-interleaving, or de-rate matching on thesignal to obtain a soft value sequence of the LDPC code.

In a possible implementation, one or more of the following may bestored:

(a) parameters used to obtain any base matrix H_(B) described in theforegoing implementations, where the base matrix H_(B) may be obtainedbased on the parameters. For example, the parameters may include one ormore of the following: a row index, a row weight, a column index, or acolumn weight of a base graph and/or a base matrix, a position of anon-zero-element in a base graph and/or a base matrix, a shift value ina base matrix, a shift value of a non-zero-element and a correspondingposition, a compensation value, a lifting factor, a lifting factor set,a base graph of a base matrix, or a code rate;

(b) any base matrix H_(B) described in the foregoing implementations;

(c) a matrix lifted from the base matrix H_(B);

(d) a base matrix obtained by performing row/column permutation on anybase matrix H_(B) described in the foregoing implementations, whererow/column permutation is row permutation, or column permutation, or rowpermutation and column permutation in this application; or

(e) a matrix lifted from the base matrix obtained by performing therow/column permutation.

In a possible implementation, an input sequence may be encoded ordecoded by using a low-density parity-check (LDPC) matrix in one or moreof the following manners during encoding or decoding:

Obtain a base matrix H_(B) based on the parameter described in theforgoing (a); and perform encoding or decoding based on the obtainedbase matrix H_(B); or perform row/column permutation based on theobtained base matrix H_(B), and perform encoding or decoding based on abase matrix obtained by performing the row/column permutation, whereencoding or decoding is performed based on the base matrix herein, andoptionally, encoding or decoding may be performed based on an liftedmatrix of the base matrix;

perform encoding or decoding based on a base matrix stored in (b) or (d)(a stored base matrix H_(B) or a stored base matrix obtained byperforming row/column permutation on a base matrix H_(B)); or performrow/column permutation on the stored base matrix, and perform encodingor decoding based on a base matrix obtained by performing the row/columnpermutation, where encoding or decoding is performed based on the basematrix herein, and optionally, encoding or decoding may be performedbased on an lifted matrix of the base matrix; or

perform encoding or decoding based on (c) or (e).

The lifting in this application may be obtaining a lifted matrix after amatrix is transformed or processed, and a lifting manner is not limitedin this application. In an implementation, the lifting may be performingcompensation processing on a matrix. For example, each shift valuegreater than or equal to 0 in a base matrix is increased or decreased bya compensation value, to obtain a compensated matrix. In anotherimplementation, the lifting may be lifting a row and a column in amatrix, to obtain a lifted matrix. In another implementation, thelifting may be converting a non-zero value in a matrix.

The storing in this application may be storing in one or more memories.The one or more memories may be separately disposed, or may beintegrated into the encoder, the decoder, a processor, a chip, thecommunications apparatus, or a terminal. Some of the one or morememories may be separately disposed, and the others may be integratedinto the decoder, a processor, a chip, the communications apparatus, ora terminal. A type of the memory may be any form of storage medium, andthe type is not limited in this application.

FIG. 6 is a schematic structural diagram of a communications apparatus600. The apparatus 600 is configured to implement the method describedin the foregoing embodiments. The descriptions in the foregoing methodembodiments are referred to for details. The communications apparatus600 may be a chip, a base station, a terminal, or another networkdevice.

The communications apparatus 600 includes one or more processors 601.The processor 601 may be a general-purpose processor, a dedicatedprocessor, or the like. For example, the processor 601 may be a basebandprocessor or a central processing unit. The baseband processor may beconfigured to perform processing on a communication protocol andcommunication data. The central processing unit may be configured tocontrol the communications apparatus (such as the base station, theterminal, or the chip), execute a software program, and process data ofthe software program.

In a possible design, the one or more processors 601 may implementfunctions of the foregoing encoder. In another possible design, theencoder may be a part of the processor 601, and the processor 601 mayimplement other functions in addition to functions of the encoder.

The communications apparatus 600 encodes an input sequence by using anLDPC matrix. A base graph of the LDPC matrix may be any base graph inthe foregoing examples or a base graph obtained by performing rowpermutation, or column permutation, or row permutation and columnpermutation on any base graph described above. Abase matrix H_(B) of theLDPC matrix may be any base matrix in the foregoing embodiment or a basematrix obtained by performing row permutation, or column permutation, orrow permutation and column permutation on any base matrix describedabove. The input sequence of the encoder may be an information bitsequence.

In a possible design, the one or more processors 601 may implementfunctions of the foregoing decoder. In another possible design, thedecoder may be a part of the processor 601.

The communications apparatus 600 may further be configured to decode aninput sequence by using an LDPC matrix. A base graph of the LDPC matrixmay be any base graph in the foregoing examples or a base graph obtainedby performing row permutation, or column permutation, or row permutationand column permutation on any base graph described above. A base matrixH_(B) of the LDPC matrix may be any base matrix in the foregoingexamples or a base matrix obtained by performing row permutation, orcolumn permutation, or row permutation and column permutation on anybase matrix described above. The input sequence of the decoder may be asoft value sequence.

Optionally, in a design, the processor 601 may also include aninstruction 603. The instruction can be run on the processor, to causethe communications apparatus 600 to perform the method described in theforegoing embodiments.

In another possible design, the communications apparatus 600 may alsoinclude a circuit, and the circuit may implement functions of theencoder, the decoder, or the encoder and the decoder in the foregoingembodiments.

Optionally, the communications apparatus 600 may include one or morememories 602. The memory stores an instruction 604, and the instructioncan be run on the processor, to cause the communications apparatus 600to perform the method described in the foregoing method embodiment.Optionally, the memory may further store data. Optionally, the processormay also store an instruction and/or data. The processor and the memorymay be separately disposed, or may be integrated together. Optionally,the one or more memories 602 may store a parameter related to a basematrix, for example, a shift value, a base graph, a matrix lifted from abase graph, rows in the base matrix, or a lifting factor. Optionally,the one or more memories 602 may store a base matrix or a matrix liftedfrom a base matrix.

Optionally, the communications apparatus 600 may further include atransceiver 605 and an antenna 606. The processor 601 may be referred toas a processing unit, and controls the communications apparatus (theterminal or the base station). The transceiver 605 may be referred to asa transceiver unit or a transceiver circuit, and is configured toimplement a transceiving function of the communications apparatus byusing the antenna 606.

Optionally, the communications apparatus 600 may further include acomponent configured to generate a transport block CRC, a component usedfor code block segmentation and CRC check, an interleaver used forinterleaving, a modulator used for modulation processing, or the like.Functions of these components may be implemented by the one or moreprocessors 601.

Optionally, the communications apparatus 600 may further include ademodulator used for demodulation, a de-interleaver used forde-interleaving, a component used for de-rate matching, or the like.Functions of these components may be implemented by the one or moreprocessors 601.

FIG. 7 is a schematic diagram of a communications system 700. Thecommunications system 700 includes a communications device 70 and acommunications device 71. The communications device 70 and thecommunications device 71 receive information data from each other andsend information data to each other. The communications device 70 andthe communications device 71 may be, for example, the communicationsapparatus 600 shown in FIG. 6 , or the communications device 70 and thecommunications device 71 each includes the communications apparatus 600shown in FIG. 6 . For example, the communications device 70 may be aterminal, and correspondingly, the communications device 71 may be abase station. For another example, the communications device 70 is abase station, and correspondingly, the communications device 71 may be aterminal.

Various illustrative logical blocks and steps that are listed in theembodiments of the present application may be implemented by usingelectronic hardware, computer software, or a combination thereof.Whether the functions are implemented by using hardware or softwaredepends on particular applications and a design requirement of theentire system. Various methods may be used to implement the describedfunctions for each particular application, but it should not beconsidered that the implementation goes beyond the scope of theembodiments of the present application.

The various illustrative logical units and circuits described in theembodiments of the present application may implement or operate thedescribed functions by using a general-purpose processor, a digitalsignal processor, an application-specific integrated circuit (ASIC), afield programmable gate array (FPGA) or another programmable logicalapparatus, a discrete gate or transistor logic, a discrete hardwarecomponent, or a design of any combination thereof. The general-purposeprocessor may be a microprocessor. Optionally, the general-purposeprocessor may be any conventional processor, controller,microcontroller, or state machine. The processor may be implemented by acombination of computing apparatuses, such as a digital signal processorand a microprocessor, a plurality of microprocessors, one or moremicroprocessors with a digital signal processor core, or any othersimilar configuration.

Steps of the methods or algorithms described in the embodiments of thepresent application may be directly embedded into hardware, aninstruction executed by a processor, or a combination thereof. Thememory may be a random access memory (RAM), a flash memory, a read-onlymemory (ROM), an erasable programmable read-only memory (EPROM) memory,an electrically erasable programmable read-only memory (EEPROM) memory,a register, a hard disk, a removable magnetic disk, a compact discread-only memory (CD-ROM), or a storage medium of any other form in theart. For example, the memory may be connected to the processor, so thatthe processor can read information from the memory and write informationto the memory. Optionally, the memory may be integrated into theprocessor. The processor and the memory may be disposed in an ASIC, andthe ASIC may be disposed in the communications apparatus (such as thebase station or the terminal). Optionally, the processor and the memorymay be disposed in different components of the communications apparatus.

With descriptions of the foregoing implementations, it is understoodthat the present application may be implemented by hardware, firmware,or a combination thereof. When the present application is implemented bya software program, the present application may be all or partiallyimplemented in a form of a computer program product. The computerprogram product includes one or more computer instructions. When thecomputer instructions are loaded and executed on the computer, theprocedure or functions according to the embodiments of the presentapplication are all or partially generated. When the present applicationis implemented by a software program, the foregoing functions may bestored in a computer readable medium or transmitted as one or moreinstructions or code in the computer readable medium. The computer maybe a general-purpose computer, a dedicated computer, a computer network,or another programmable apparatus. The computer instruction may bestored in a computer readable storage medium, or may be transmitted fromone computer readable storage medium to another. The computer readablemedium includes a computer storage medium and a communications medium,where the communications medium includes any medium that enables acomputer program to be transmitted from one place to another. Thestorage medium may be any available medium accessible to a computer. Thefollowing provides an example but does not impose a limitation: Thecomputer readable medium may include a RAM, a ROM, an EEPROM, a CD-ROM,or another optical disc storage or disk storage medium, or anothermagnetic storage device, or any other medium that can carry or storeexpected program code in a form of an instruction or a data structureand can be accessed by a computer. In addition, any connection may beappropriately defined as a computer readable medium. For example, ifsoftware is transmitted from a website, a server, or another remotesource by using a coaxial cable, an optical fiber/cable, a twisted pair,a digital subscriber line (DSL), or wireless technologies such asinfrared ray, radio, and microwave, the coaxial cable, opticalfiber/cable, twisted pair, DSL, or wireless technologies such asinfrared ray, radio, and microwave are included in a definition of amedium to which they belong. For example, a disk or a disc used by thepresent application includes a compact disc (CD), a laser disc, anoptical disc, a digital versatile disc (DVD), a floppy disk, and aBlu-ray disc, where the disk generally copies data by a magnetic means,and the disc copies data optically by a laser means. The foregoingcombination should also be included in the protection scope of thecomputer readable medium.

In this application, “/” indicates and/or. For example,encoding/decoding indicates encoding, decoding, or encoding anddecoding.

In summary, what is described above is merely embodiments of thetechnical solutions of the present application, but is not intended tolimit the protection scope of the present application. Any modification,equivalent replacement, or improvement made without departing from theprinciple of the present application shall fall within the protectionscope of the present application.

The invention claimed is:
 1. An apparatus, comprising: at least oneprocessor; wherein the at least one processor is configured to: obtainan input sequence comprising K bits, wherein K is a positive integer;encode the input sequence using an encoding matrix H to obtain anencoded sequence; and output the encoded sequence; wherein the encodingmatrix H is determined according to a low density parity check (LDPC)base matrix and a lifting factor Z; wherein the LDPC base matrixcomprises m rows and n columns, wherein m and n are integers; whereineach element in the LDPC base matrix corresponds to a respective rowindex i and a respective column index j, wherein 0≤i<m, and 0≤j<n; andwherein at least the following elements in the LDPC base matrixcorrespond to non-zero elements, and other elements in each followingrow correspond to zero elements: i=0, j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12,13, 15, 16, 18, 19, 20, 21, 22, or 23; i=1, j=0, 2, 3, 4, 5, 7, 8, 9,11, 12, 14, 15, 16, 17, 19, 21, 22, 23, or 24; i=2, j=0, 1, 2, 4, 5, 6,7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, or 25; or i=3, j=0, 1, 3,4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, or
 25. 2. Theapparatus according to claim 1, wherein the following elements in theLDPC base matrix correspond to non-zero elements, and other elements inthe following row correspond to zero elements: i=4, j=0, 1 or
 26. 3. Theapparatus according to claim 2, wherein 5≤m≤46, and 27≤n≤68.
 4. Theapparatus according to claim 1, wherein m=46 and n=68, and the followingelements in the LDPC base matrix correspond to non-zero elements, andother elements in the following rows correspond to zero elements: i=0,j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, or23; i=1, j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22,23, or 24; i=2, j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19,20, 24, or 25; i=3, j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17,18, 20, 21, 22, or 25; i=4, j=0, 1 or 26; i=5, j=0, 1, 3, 12, 16, 21,22, or 27; i=6, j=0, 6, 10, 11, 13, 17, 18, 20, or 28; i=7, j=0, 1, 4,7, 8, 14, or 29; i=8, j=0, 1, 3, 12, 16, 19, 21, 22, 24, or 30; i=9,j=0, 1, 10, 11, 13, 17, 18, 20, or 31; i=10, j=1, 2, 4, 7, 8, 14, or 32;i=11, j=0, 12, 16, 21, 22, 23, or 33; i=12, j=0, 1, 10, 11, 13, 18, or34; i=13, j=0, 3, 7, 20, 23, or 35; i=14, j=0, 12, 15, 16, 17, 21, or36; i=15, j=0, 1, 10, 13, 18, 25, or 37; i=16, j=1, 3, 11, 20, 22, or38; i=17, j=0, 14, 16, 17, 21, or 39; i=18, j=1, 12, 13, 18, 19, or 40;i=19, j=0, 1, 7, 8, 10, or 41; i=20, j=0, 3, 9, 11, 22, or 42; i=21,j=1, 5, 16, 20, 21, or 43; i=22, j=0, 12, 13, 17, or 44; i=23, j=1, 2,10, 18, or 45; i=24, j=0, 3, 4, 11, 22, or 46; i=25, j=1, 6, 7, 14, or47; i=26, j=0, 2, 4, 15, or 48; i=27, j=1, 6, 8, or 49; i=28, j=0, 4,19, 21, or 50; i=29, j=1, 14, 18, 25, or 51; i=30, j=0, 10, 13, 24, or52; i=31, j=1, 7, 22, 25, or 53; i=32, j=0, 12, 14, 24, or 54; i=33,j=1, 2, 11, 21, or 55; i=34, j=0, 7, 15, 17, or 56; i=35, j=1, 6, 12,22, or 57; i=36, j=0, 14, 15, 18, or 58; i=37, j=1, 13, 23, or 59; i=38,j=0, 9, 10, 12, or 60; i=39, j=1, 3, 7, 19, or 61; i=40, j=0, 8, 17, or62; i=41, j=1, 3, 9, 18, or 63; i=42, j=0, 4, 24, or 64; i=43, j=1, 16,18, 25, or 65; i=44, j=0, 7, 9, 22, or 66; or i=45, j=1, 6, 10, or 67.5. The apparatus according to claim 1, wherein each zero elementcorresponds to a Z*Z zero matrix in the encoding matrix H, each non-zeroelement corresponds to a Z*Z circular permutation matrix I(P_(i,j)) inthe encoding matrix H, wherein the circular permutation matrixI(P_(i,j)) is equal to a matrix obtained by circularly shifting an Z*Zidentity matrix to the right for P_(i,j) times.
 6. The apparatusaccording to claim 5, wherein P_(i,j)=mod (V_(i,j), Z), V_(i,j) is ashift value corresponding to a lifting factor set index of Z, V_(i,j) isan integer, and V_(i,j)≥0.
 7. The apparatus according to claim 1,wherein the lifting factor Z is a minimum of a plurality of liftingfactors, and Z satisfies 22*Z≥K.
 8. A method, comprising: obtaining aninput sequence comprising K bits, wherein K is a positive integer;encoding the input sequence using an encoding matrix H to obtain anencoded sequence; and outputting the encoded sequence; wherein theencoding matrix H is determined according to a low density parity check(LDPC) base matrix and a lifting factor Z; wherein the LDPC base matrixcomprises m rows and n columns, wherein m and n are integers; whereineach element in the LDPC base matrix corresponds to a respective rowindex i and a respective column index j, wherein 0≤i<m, and 0≤j<n; andwherein at least the following elements in the LDPC base matrixcorrespond to non-zero elements, and other elements in each followingrow correspond to zero elements: i=0, j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12,13, 15, 16, 18, 19, 20, 21, 22, or 23; i=1, j=0, 2, 3, 4, 5, 7, 8, 9,11, 12, 14, 15, 16, 17, 19, 21, 22, 23, or 24; i=2, j=0, 1, 2, 4, 5, 6,7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, or 25; or i=3, j=0, 1, 3,4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, or
 25. 9. Themethod according to claim 8, wherein the following elements in the LDPCbase matrix correspond to non-zero elements, and other elements in thefollowing row correspond to zero elements: i=4, j=0, 1 or
 26. 10. Themethod according to claim 9, wherein 5≤m≤46, and 27≤n≤68.
 11. The methodaccording to claim 8, wherein m=46 and n=68, and the following elementsin the LDPC base matrix correspond to non-zero elements, and otherelements in the following rows correspond to zero elements: i=0, j=0, 1,2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, or 23; i=1,j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, or 24;i=2, j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, or25; i=3, j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21,22, or 25; i=4, j=0, 1 or 26; i=5, j=0, 1, 3, 12, 16, 21, 22, or 27;i=6, j=0, 6, 10, 11, 13, 17, 18, 20, or 28; i=7, j=0, 1, 4, 7, 8, 14, or29; i=8, j=0, 1,3, 12, 16, 19, 21, 22, 24, or 30; i=9, j=0, 1, 10, 11,13, 17, 18, 20, or 31; i=10, j=1, 2, 4, 7, 8, 14, or 32; i=11, j=0, 1,12, 16, 21, 22, 23, or 33; i=12, j=0, 1, 10, 11, 13, 18, or 34; i=13,j=0, 3, 7, 20, 23, or 35; i=14, j=0, 12, 15, 16, 17, 21, or 36; i=15,j=0, 1, 10, 13, 18, 25, or 37; i=16, j=1, 3, 11, 20, 22, or 38; i=17,j=0, 14, 16, 17, 21, or 39; i=18, j=1, 12, 13, 18, 19, or 40; i=19, j=0,1, 7, 8, 10, or 41; i=20, j=0, 3, 9, 11, 22, or 42; i=21, j=1, 5, 16,20, 21, or 43; i=22, j=0, 12, 13, 17, or 44; i=23, j=1, 2, 10, 18, or45; i=24, j=0, 3, 4, 11, 22, or 46; i=25, j=1, 6, 7, 14, or 47; i=26,j=0, 2, 4, 15, or 48; i=27, j=1, 6, 8, or 49; i=28, j=0, 4, 19, 21, or50; i=29, j=1, 14, 18, 25, or 51; i=30, j=0, 10, 13, 24, or 52; i=31,j=1, 7, 22, 25, or 53; i=32, j=0, 12, 14, 24, or 54; i=33, j=1, 2, 11,21, or 55; i=34, j=0, 7, 15, 17, or 56; i=35, j=1, 6, 12, 22, or 57;i=36, j=0, 14, 15, 18, or 58; i=37, j=1, 13, 23, or 59; i=38, j=0, 9,10, 12, or 60; i=39, j=1, 3, 7, 19, or 61; i=40, j=0, 8, 17, or 62;i=41, j=1, 3, 9, 18, or 63; i=42, j=0, 4, 24, or 64; i=43, j=1, 16, 18,25, or 65; i=44, j=0, 7, 9, 22, or 66; or i=45, j=1, 6, 10, or
 67. 12.The method according to claim 8, wherein each zero element correspondsto a Z*Z zero matrix in the encoding matrix H, each non-zero elementcorresponds to a Z*Z circular permutation matrix I(P_(i,j)) in theencoding matrix H, wherein the circular permutation matrix I(P_(i,j)) isequal to a matrix obtained by circularly shifting an Z*Z identity matrixto the right for P_(i,j) times.
 13. The method according to claim 12,wherein P_(i,j)=mod (V_(i,j), Z), V_(i,j) is a shift value correspondingto a lifting factor set index of Z, V_(i,j) is an integer, andV_(i,j)≥0.
 14. The method according to claim 8, wherein the liftingfactor Z is a minimum of a plurality of lifting factors, and Z satisfies22*Z≥K.
 15. A non-transitory computer-readable storage medium havingprocessor-executable instructions stored thereon, wherein theprocessor-executable instructions, when executed by a processor,facilitate performance of steps comprising: obtaining an input sequencecomprising K bits, wherein K is a positive integer; encoding the inputsequence using an encoding matrix H to obtain an encoded sequence; andoutputting the encoded sequence; wherein the encoding matrix H isdetermined according to a low density parity check (LDPC) base matrixand a lifting factor Z; wherein the LDPC base matrix comprises m rowsand n columns, wherein m and n are integers; wherein each element in theLDPC base matrix corresponds to a respective row index i and arespective column index j, wherein 0≤i<m, and 0≤j<n; and wherein atleast the following elements in the LDPC base matrix correspond tonon-zero elements, and other elements in each following row correspondto zero elements: i=0, j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16,18, 19, 20, 21, 22, or 23; i=1, j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14,15, 16, 17, 19, 21, 22, 23, or 24; i=2, j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10,13, 14, 15, 17, 18, 19, 20, 24, or 25; or i=3, j=0, 1, 3, 4, 6, 7, 8,10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, or
 25. 16. Thenon-transitory computer-readable storage medium according to claim 15,wherein the following elements in the LDPC base matrix correspond tonon-zero elements, and other elements in the following row correspond tozero elements: i=4, j=0, 1 or
 26. 17. The non-transitorycomputer-readable storage medium according to claim 16, wherein 5≤m≤46,and 27≤n≤68.
 18. The non-transitory computer-readable storage mediumaccording to claim 15, wherein m=46 and n=68, and the following elementsin the LDPC base matrix correspond to non-zero elements, and otherelements in the following rows correspond to zero elements: i=0, j=0, 1,2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, or 23; i=1,j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, or 24;i=2, j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, or25; i=3, j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21,22, or 25; i=4, j=0, 1 or 26; i=5, j=0, 1, 3, 12, 16, 21, 22, or 27;i=6, j=0, 6, 10, 11, 13, 17, 18, 20, or 28; i=7, j=0, 1, 4, 7, 8, 14, or29; i=8, j=0, 1,3, 12, 16, 19, 21, 22, 24, or 30; i=9, j=0, 1, 10, 11,13, 17, 18, 20, or 31; i=10, j=1, 2, 4, 7, 8, 14, or 32; i=11, j=0, 1,12, 16, 21, 22, 23, or 33; i=12, j=0, 1, 10, 11, 13, 18, or 34; i=13,j=0, 3, 7, 20, 23, or 35; i=14, j=0, 12, 15, 16, 17, 21, or 36; i=15,j=0, 1, 10, 13, 18, 25, or 37; i=16, j=1, 3, 11, 20, 22, or 38; i=17,j=0, 14, 16, 17, 21, or 39; i=18, j=1, 12, 13, 18, 19, or 40; i=19, j=0,1, 7, 8, 10, or 41; i=20, j=0, 3, 9, 11, 22, or 42; i=21, j=1, 5, 16,20, 21, or 43; i=22, j=0, 12, 13, 17, or 44; i=23, j=1, 2, 10, 18, or45; i=24, j=0, 3, 4, 11, 22, or 46; i=25, j=1, 6, 7, 14, or 47; i=26,j=0, 2, 4, 15, or 48; i=27, j=1, 6, 8, or 49; i=28, j=0, 4, 19, 21, or50; i=29, j=1, 14, 18, 25, or 51; i=30, j=0, 10, 13, 24, or 52; i=31,j=1, 7, 22, 25, or 53; i=32, j=0, 12, 14, 24, or 54; i=33, j=1, 2, 11,21, or 55; i=34, j=0, 7, 15, 17, or 56; i=35, j=1, 6, 12, 22, or 57;i=36, j=0, 14, 15, 18, or 58; i=37, j=1, 13, 23, or 59; i=38, j=0, 9,10, 12, or 60; i=39, j=1, 3, 7, 19, or 61; i=40, j=0, 8, 17, or 62;i=41, j=1, 3, 9, 18, or 63; i=42, j=0, 4, 24, or 64; i=43, j=1, 16, 18,25, or 65; i=44, j=0, 7, 9, 22, or 66; or i=45, j=1, 6, 10, or
 67. 19.The non-transitory computer-readable storage medium according to claim15, wherein each zero element corresponds to a Z*Z zero matrix in theencoding matrix H, each non-zero element corresponds to a Z*Z circularpermutation matrix I(P_(i,j)) in the encoding matrix H, wherein thecircular permutation matrix I(P_(i,j)) is equal to a matrix obtained bycircularly shifting an Z*Z identity matrix to the right for P_(i,j)times.
 20. The non-transitory computer-readable storage medium accordingto claim 19, wherein P_(i,j)=mod (V_(i,j), Z), V_(i,j) is a shift valuecorresponding to a lifting factor set index of Z, V_(i,j) is an integer,and V_(i,j)≥0.
 21. The non-transitory computer-readable storage mediumaccording to claim 15, wherein the lifting factor Z is a minimum of aplurality of lifting factors, and Z satisfies 22*Z≥K.